偏微分方程

张祖锦

目录

  • Zujin Zhang's Publications
    • ● Links and Pdfs
  • Research
    • ● 210521Responses to  ZAMP-D-20-00709
    • ● 210603Responses to 344/20 (12445)
    • ● Zhang Yali‘s master
    • ● Wang Sinan's master
  • Tsai-Lectures on NSE
    • ● Chapter 1 Introduction
    • ● Chapter 2 Steady states
    • ● Chapter 3 Weak solutions
    • ● Chapter 4 Strong solutions
    • ● Chapter 5 Mild solutions
    • ● Chapter 6 Partial regularity
    • ● Chapter 7 Bondary value problems and bifurcation
    • ● Chapter 8 Self-similar solutions
    • ● Chapter 9 The uniform L3 class
    • ● Chapter 10 Axisymmetric flows
  • Evans PDE 6 Second-order Elliptic Equations
    • ● 6.1 Definitions
    • ● 6.2 Existence of weak solutions
    • ● 6.3 Regularity
    • ● 6.4 Maximum principle
    • ● 6.5 Eigenvalues and eigenfunctions
    • ● 6.6 Problems
  • Evans PDE 5 Sobolev spaces
    • ● pdf and video
  • Evans PDE Chapter 5 and Appendix by Zujin Zhang
    • ● Introduction
    • ● 5.1 H\"older spaces
    • ● 5.2 Sobolev spaces
      • ● 5.2.1 Weak derivatives
      • ● 5.2.2 Defintion of Sobolev spaces
      • ● 5.2.3 Elementary properties
    • ● 5.3 Approximation
      • ● 5.3.1 Interior approximation by smooth functions
      • ● 5.3.2 Approximation by smooth functions
      • ● 5.3.3 Global approximation by smooth functions
    • ● 5.4 Extensions
    • ● 5.5 Traces
    • ● 5.6 Sobolev inequalities
      • ● 5.6.1 Gagliardo-Nirenberg-Sobolev inequality
      • ● 5.6.2 Morrey's inequality
      • ● 5.6.3 General Sobolev inequalities
    • ● 5.7 Compactness
    • ● 5.8 Additional Topics
      • ● 5.8.1 Poincar'e's inequality
      • ● 5.8.2 Difference quotients
      • ● 5.8.3 Differentiable  a.e.
      • ● 5.8.4 Hardy's inequality
      • ● 5.8.5 Fourier transform methods
    • ● 5.9 Other spaces of functions
      • ● 5.9.1 The space H^{-1}
      • ● 5.9.2 Spaces involving time
    • ● 5.10 Problems
      • ● 5.10.01 Holder spaces are Banach spaces
      • ● 5.10.02 An interpolation inequality for Holder norms
      • ● 5.10.03 A parameter of Sobolev functions
      • ● 5.10.04 Sobolev spaces on an open interval
      • ● 5.10.05 A cut-off function
      • ● 5.10.06 Partition of unity
      • ● 5.10.07 A new proof of the trace theorem
      • ● 5.10.08 No Trace operator for Lebesgue spaces
      • ● 5.10.09 An interpolation inequality
      • ● 5.10.10 Two interpolation inequalities
      • ● 5.10.11 Sobolev functions with weak derivative a.e. 0
      • ● 5.10.12 An counterexample for difference quotients. p=1 case
      • ● 5.10.13 An example showing W^{1,\infty} is a proper subset of Lip
      • ● 5.10.14 W^{1,n} is not ess. bounded
      • ● 5.10.15 A Poincar'e-type inequality
      • ● 5.10.16 Variant of Hardy's inequality
      • ● 5.10.17 Chain rule
      • ● 5.10.18 The positive/negative part of Sobolev functions
      • ● 5.10.19 Alternative proof of Problem 18 (3)
      • ● 5.10.20 For s>n/2, H^s is ess bounded
      • ● 5.10.21 For s>n/2, H^s is a Banach algebra
    • ● Appendix
      • ● A.1、Notation  for matrices
      • ● A.2、 Geometric noation
      • ● A.3、 Notation for functions
      • ● A.4、 Vector-valued functions
      • ● A.5、 Notation for estimates
      • ● A.6、 Some comments about notation
      • ● B.1、 Convex functions
      • ● B.2、 Useful inequalities
      • ● C.1、 Boundaries
      • ● C.2、 Gauss-Green theorem
      • ● C.3、 Polar coordinates, coarea formula
      • ● C.4、 Moving regions
      • ● C.5、 Convolution and smoothing
      • ● C.6、 Inverse function theorem
      • ● C.7、 Implicit function theorem
      • ● C.8、 Uniform convergence
      • ● D.1、 Banach spaces
      • ● D.2、 Hilbert spaces
      • ● D.3、 Bounded linear operaters
      • ● D.4. Weak convergence
      • ● D.5、 Compact operators, Fredholm theory
      • ● D.6. Symmetric operators
      • ● E.1. Lebesgue measure
      • ● E.2. Measurable functions and integration
      • ● E.3. Convergence theorems for integrals
      • ● E.4. Differentiation
      • ● E.5、 Banach space-valued functions
  • The three-dimensional Navier-Stokes equations
    • ● the pdf of the book
    • ● NSE180912
    • ● NSE180918
    • ● NSE180919
    • ● NSE180926
    • ● NSE181009
    • ● NSE181010
    • ● NSE181016
    • ● NSE181017
    • ● NSE181024
    • ● NSE181031
    • ● NSE181107
    • ● NSE181114
    • ● NSE181121
    • ● NSE181128
    • ● NSE181212
    • ● NSE190226
    • ● NSE190305
    • ● NSE190312
    • ● NSE190319
    • ● NSE190326
    • ● NSE190402
    • ● NSE190409
    • ● NSE190416
    • ● NSE190423
  • Fourier分析与偏微分方程
    • ● the pdf of the book
    • ● Real Analysis
    • ● Littlewood-Paley theory
      • ● Functions with compactly supported Fourier transform
      • ● Dyadic partition of unity
      • ● Homogeneous Besov spaces
      • ● Characterizations of homogeneous Besov spaces
      • ● Besov spaces, Lebesgue spaces, and refined inequalities
      • ● Homogeneous paradifferential calculus
      • ● Nonhomogeneous Besov spaces
  • 硕士培养过程
    • ● 210603袁伟俊硕士论文答辩预演
    • ● 210615科研方法论
Links and Pdfs

Zhang, Zujin. Regularity criterion for the system modeling the flow of liquid crystals via the direction of velocity. Comm. Appl. Nonlinear Anal. 17 (2010), no. 3, 55--60.  link 

Zhang, Zujin. Remarks on the regularity criteria for generalized MHD equations. J. Math. Anal. Appl. 375 (2011), no. 2, 799--802.  link 

Zhang, Zujin; Wu, Xinglong; Lu, Ming. On the uniqueness of strong solution to the incompressible Navier-Stokes equations with damping. J. Math. Anal. Appl. 377 (2011), no. 1, 414--419.  link 

Zhang, Zujin; Yao, Zheng-an; Wang, Xiaofeng. A regularity criterion for the 3D magneto-micropolar fluid equations in Triebel-Lizorkin spaces. Nonlinear Anal. 74 (2011), no. 6, 2220--2225.  link 

Zhang, Zujin; Yao, Zheng-an; Lu, Ming; Ni, Lidiao. Some Serrin-type regularity criteria for weak solutions to the Navier-Stokes equations. J. Math. Phys. 52 (2011), no. 5, 053103, 7 pp.  link 

Zhang, Zujin; Wang, Xiaofeng; Yao, Zheng-an. Remarks on regularity criteria for the weak solutions of liquid crystals. J. Evol. Equ. 12 (2012), no. 4, 801--812.  link 

Lu, Ming; Du, Yi; Yao, Zheng-an; Zhang, Zujin. A blow-up criterion for the 3D compressible MHD equations. Commun. Pure Appl. Anal. 11 (2012), no. 3, 1167--1183.  link 

Guo, Congchong; Zhang, Zujin; Wang, Jialin. Regularity criteria for the 3D magneto-micropolar fluid equations in Besov spaces with negative indices. Appl. Math. Comput. 218 (2012), no. 21, 10755--10758.  link 

Zhang, Zujin. A Serrin-type regularity criterion for the Navier-Stokes equations via one velocity component. Commun. Pure Appl. Anal. 12 (2013), no. 1, 117--124.  link 

Zhang, Zujin; Yao, Zheng-an; Li, Peng; Guo, Congchong; Lu, Ming. Two new regularity criteria for the 3D Navier-Stokes equations via two entries of the velocity gradient tensor. Acta Appl. Math. 123 (2013), 43--52.  link 

Zhang, Zujin; Li, Peng; Yu, Gaohang. Regularity criteria for the 3D MHD equations via one directional derivative of the pressure. J. Math. Anal. Appl. 401 (2013), no. 1, 66--71.  link 

Zhang, Zujin; Gala, Sadek. Osgood type regularity criterion for the 3D Newton-Boussinesq equation. Electron. J. Differential Equations 2013, No. 223, 6 pp.  link 

Zhang, Zujin; Wang, Xiaofeng; Yao, Zheng-an. On a fractional nonlinear hyperbolic equation arising from relative theory. Abstr. Appl. Anal. 2013, Art. ID 548562, 6 pp.  link 

Zhang, Zujin; Ouyang, Xiqin; Zhong, Dingxing; Qiu, Shulin. Remarks on the regularity criteria for the 3D MHD equations in the multiplier spaces. Bound. Value Probl. 2013, 2013:270, 7 pp.  link 

Zhong, Ding Xing; Sun, Hong An; Zhang, Zujin. Hypersurfaces in with three distinct constant para-Blaschke eigenvalues. (Chinese) Acta Math. Sinica (Chin. Ser.) 56 (2013), no. 5, 751--766.  link

Li, Peng; Li, Shuai-Jie; Yao, Zheng-An; Zhang, Zujin. Two anisotropic fourth-order partial differential equations for image inpainting. IET Image Process. 7 (2013), no. 3, 260--269.  link

Zhang, Zujin; Li, Peng; Zhong, Dingxing. Navier-Stokes equations with regularity in two entries of the velocity gradient tensor. Appl. Math. Comput. 228 (2014), 546--551.  link

Zhang, Zujin; Zhong, Dingxing; Hu, Lin. A new regularity criterion for the 3D Navier-Stokes equations via two entries of the velocity gradient tensor. Acta Appl. Math. 129 (2014), 175--181.  link

Zhang, Zujin. A remark on the regularity criterion for the 3D Boussinesq equations involving the pressure gradient. Abstr. Appl. Anal. 2014, Art. ID 510924, 4 pp.  link

Zhang, Zujin. A remark on the regularity criterion for the 3D Navier-Stokes equations involving the gradient of one velocity component. J. Math. Anal. Appl. 414 (2014), no. 1, 472--479.  link

Zhang, Zujin; Tang, Tong; Liu, Lihan. An Osgood type regularity criterion for the liquid crystal flows. NoDEA Nonlinear Differential Equations Appl. 21 (2014), no. 2, 253--262.  link

Zhang, Zujin; Wang, Xiaofeng; Yao, Zheng-an. On the weak solution to a fractional nonlinear Schr"odinger equation. Abstr. Appl. Anal. 2014, Art. ID 569693, 6 pp.  link

Zhang, Zujin. A logarithmically improved regularity criterion for the 3D Boussinesq equations via the pressure. Acta Appl. Math. 131 (2014), 213--219.  link

Zhang, Zujin. Global regularity for the 2D micropolar fluid flows with mixed partial dissipation and angular viscosity. Abstr. Appl. Anal. 2014, Art. ID 709746, 6 pp.  link

Zhang, Zujin; Alzahrani, Faris; Hayat, Tasawar; Zhou, Yong. Two new regularity criteria for the Navier-Stokes equations via two entries of the velocity Hessian tensor. Appl. Math. Lett. 37 (2014), 124--130.  link

Zhang, Zujin. An improved regularity criterion for the 3D Navier-Stokes equations in terms of two entries of the velocity gradient. (Chinese) Acta Math. Sci. Ser. A Chin. Ed. 34 (2014), no. 5, 1327--1335.  link

Zhang, Zujin. Some regularity criteria for the 3D Boussinesq equations in the class . ISRN Appl. Math. 2014, Art. ID 564758, 4 pp.  link

Zhang, Zujin; Tang, Tong; Zhang, Fumin. A remark on the regularity criterion for the MHD equations via two components in Morrey-Campanato spaces. Journal of Difference Equations, 2014, Art. ID  364269, 5 pp.  link

Zhang, Zujin. MHD equations with regularity in one direction. International Journal of Partial Differential Equations. 2014,  Art. ID  213083, 6 pp.  link

Wu, Qiang; Hu, Lin; Zhang, Zujin. Convergence and stability of balanced methods for stochastic delay integro-differential equations. Appl. Math. Comput. 237 (2014), 446--460.  link

Benbernou, Samia; Terbeche, Mekki; Ragusa, Maria Alessandra; Zhang, Zujin. A note on the regularity criterion for 3D MHD equations in space. Appl. Math. Comput. 238 (2014), 245--249.  link

Zhong, Dingxing; Zhang, Zujin; Tao, Lingyang. The hypersurfaces with parallel Lagueree form in . Acta Mathematica Sinica, Chinese Series, 57 (2014), 21--32.  link

Zhang, Zujin; Yang, Xian. On the regularity criterion for the Navier-Stokes equations involving the diagonal entry of the velocity gradient. Nonlinear Anal. 122 (2015), 169--175.  link

Zhang, Zujin. Remarks on the global regularity criteria for the 3D MHD equations via two components. Z. Angew. Math. Phys. 66 (2015), no. 3, 977--987.  link

Zhang, Zujin. An almost Serrin-type regularity criterion for the Navier-Stokes equations involving the gradient of one velocity component. Z. Angew. Math. Phys. 66 (2015), no. 4, 1707--1715.  link

Zhang, Zujin; Yang, Xian. A note on the regularity criterion for the 3D Navier-Stokes equations via the gradient of one velocity component. J. Math. Anal. Appl. 432 (2015), no. 1, 603--611.  link

Zhang, Zujin; Yang, Xian. A regularity criterion for the 3D density-dependent incompressible flow of liquid crystals with vacuum. Ann. Polon. Math. 115 (2015), no. 2, 165--177.  link

Zhang, Zujin. Regularity criteria for the 3D magneto-micropolar fluid equations via the direction of the velocity. Proc. Indian Acad. Sci. Math. Sci. 125 (2015), no. 1, 37--43.  link

Zhang, Zujin. Navier-Stokes equations with regularity in one directional derivative of the pressure. Math. Methods Appl. Sci. 38 (2015), no. 17, 4019--4023.  link

Zhang, Zujin; Hong, Pingzhou; Zhong, Dingxing; Qiu, Shulin. A regularity criterion for the 3D MHD equations in terms of the gradient of the pressure in the multiplier spaces. Arab. J. Math. (Springer) 4 (2015), no. 2, 153--157.  link

Zhang, Zujin; Yang, Xian; Qiu, Shulin. Remarks on Liouville type result for the 3D Hall-MHD system. J. Partial Differ. Equ. 28 (2015), no. 3, 286--290.  link

Xu, Xiaojing; Ye, Zhuan; Zhang, Zujin. Remark on an improved regularity criterion for the 3D MHD equations. Appl. Math. Lett. 42 (2015), 41--46.  link

Hu, Lin; Wu, Qiang; Xu Qingcui; Zhang, Zujin; Li, Huacan. Numerical Analysis of Balanced Methods for the Impulsive Stochastic Differential Equations, Journal of Donghua University (English Edition), 32 (2015), no. 4, 626—635.  link

Tang, Tong; Zhang, Zujin. Blow-Up of Smooth Solution to the Compressible Navier-Stokes-Poisson Equations. Bull. Malays. Math. Sci. Soc. 39 (2016), no. 4, 1487--1497.  link

Zhang, Zujin; Yang, Xian; Qiu, Shulin. A regularity condition for the density-dependent magnetohydrodynamic equations in BMO space. Proc. Jangjeon Math. Soc. 19 (2016), no. 1, 125--133.  link

Zhang, Zujin; Ouyang Xiqin; Yang, Xian. Navier-Stokes equations with anisotropic regularity in one velocity component. Proc. Jangjeon Math. Soc. 19 (2016), 465--476.  link

Zhang, Zujin; Zhong, Dingxing; Gui, Shaohui. Density-dependent magnetohydrodynamic equations with velocity and magnetic fields in Besov spaces of negative order. J. Math. Res. Appl. 36 (2016), no. 6, 682--688.  link

Zhang, Zujin. Global regularity criteria for the -dimensional Boussinesq equations with fractional dissipation. Electron. J. Differential Equations 2016, Paper No. 99, 5 pp.  link

Zhang, Zujin; Yang, Xian. Global regularity for the 3D MHD system with damping. Colloq. Math. 145 (2016), no. 1, 107--110.  link

Zhang, Zujin; Yang, Xian. Remarks on the blow-up criterion for the MHD system involving horizontal components or their horizontal gradients. Ann. Polon. Math. 116 (2016), no. 1, 87--99.  link

Zhang, Zujin. Remarks on regularity criteria for the Navier-Stokes equations with axisymmetric data. Ann. Polon. Math. 117 (2016), no. 2, 181--196.  link

Zhang, Zujin. A logarithmically improved regularity criterion for the 3D MHD system involving the velocity field in homogeneous Besov spaces. Ann. Polon. Math. 118 (2016), no. 1, 51--57.  link

Zhang, Zujin. 3D Density-Dependent Boussinesq Equations with Velocity Field in BMO Spaces. Acta Appl. Math. 142 (2016), 1--8.  link

Zhang, Zujin; Zhou, Yong. On regularity criteria for the 3D Navier-Stokes equations involving the ratio of the vorticity and the velocity. Comput. Math. Appl. 72 (2016), no. 9, 2311--2314.  link

Zhang, Zujin. A regularity criterion for the three-dimensional micropolar fluid system in homogeneous Besov spaces. Electron. J. Qual. Theory Differ. Equ. 2016, Paper No. 104, 6 pp.  link

Zhang, Zujin; Yang, Xian. Navier-Stokes equations with vorticity in Besov spaces of negative regular indices. J. Math. Anal. Appl. 440 (2016), no. 1, 415--419.  link

Zhang, Zujin. A remark on the blow-up criterion for the 3D Hall-MHD system in Besov spaces. J. Math. Anal. Appl. 441 (2016), no. 2, 692--701.  link

Zhang, Zujin. On weighted regularity criteria for the axisymmetric Navier-Stokes equations. Appl. Math. Comput. 296 (2017), 18--22.  link

Ye, Zhuan; Zhang, Zujin. A remark on regularity criterion for the 3D Hall-MHD equations based on the vorticity. Appl. Math. Comput. 301 (2017), 70--77.  link

Zhang, Zujin; Ouyang, Xiqin; Yang, Xian. Refined a priori estimates for the axisymmetric Navier-Stokes equations. J. Appl. Anal. Comput. 7 (2017), no. 2, 554--558.  link

Zhang, Zujin. Generalized MHD System with Velocity Gradient in Besov Spaces of Negative Order. Acta Appl. Math. 149 (2017), 139--144.   link

Zhang, Zujin; Zhong, Dingxing; Huang, Xiantong. A refined regularity criterion for the Navier-Stokes equations involving one non-diagonal entry of the velocity gradient. J. Math. Anal. Appl. 453 (2017), no. 2, 1145--1150.  link

Zhang, Zujin; Yao, Zheng-an. 3D axisymmetric MHD system with regularity in the swirl component of the vorticity. Comput. Math. Appl. 73 (2017), no. 12, 2573--2580.  link

张祖锦, 杨兰萍, 李文鑫. 拓扑学中凝聚点的几个等价定义[J]. 赣南师范大学学报, 2017 , 03 : 6--7.  link

Zhang, Zujin; Zhong, Dingxing; Gao, Shujing; Qiu, Shulin. Fundamental Serrin type regularity criteria for 3D MHD fluid passing through the porous medium. Filomat 31 (2017), no. 5, 1287--1293.  link

Zhang, Zujin. Refined regularity criteria for the MHD system involving only two components of the solution. Appl. Anal. 96 (2017), no. 12, 2130--2139.  link

Gao, Shujing; Xia, Lijun; Wang, Jialin; Zhang, Zujin. Modeling the effects of cross-protection control in plant disease with seasonality. Int. J. Biomath. 10 (2017), no. 6, 1750088, 24 pp.  link

Zhang, Zujin. Blow-up criterion of strong solutions to the 3D ghost effect system in Besov spaces with negative indices. ZAMM Z. Angew. Math. Mech. 97 (2017), no. 5, 576--585.  link

Gala, Sadek; Ragusa, Maria Alessandra; Zhang, Zujin. A Regularity Criterion in Terms of Pressure for the 3D Viscous MHD Equations. Bull. Malays. Math. Sci. Soc. 40 (2017), no. 4, 1677--1690.   link

Zhang, Zujin. A pointwise regularity criterion for axisymmetric Navier-Stokes system. J. Math. Anal. Appl. 461 (2018), no. 1, 1--6.   link

Zhang, Zujin. On the blow-up criterion for the quasi-geostrophic equations in homogeneous Besov spaces. Comput. Math. Appl. 75 (2018), no. 3, 1038--1043.  link

Zhang, Zujin. Regularity criteria for the three dimensional Ericksen-Leslie system in homogeneous Besov spaces. Comput. Math. Appl. 75 (2018), no. 3, 1060--1065.   link

Zhang, Zujin. An improved regularity criterion for the Navier-Stokes equations in terms of one directional derivative of the velocity field. Bull. Math. Sci. 8 (2018), no. 1, 33--47.   link

Zhang, Zujin. Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component. Czechoslovak Math. J. 68 (2018), no. 1, 219--225.   link

Zhang, Zujin; Li, Jinlu; Yao, Zheng-an. A remark on the global regularity criterion for the 3D Navier-Stokes equations based on end-point Prodi-Serrin conditions. Appl. Math. Lett. 83 (2018), 182--187.  link

Zhang, Zujin; Wu, Chupeng; Yao, Zheng-an. Remarks on global regularity for the 3D MHD system with damping. Appl. Math. Comput. 333 (2018), 1--7.  link

张祖锦, 张程荣, 陈媛, 胡燕玲. 一个数学分析定理在点集拓扑中的推广[J]. 赣南师范大学学报, 2018, 03 : 8--9.  link

Zhang, Zujin. 3D Hall-MHD system with vorticity in Besov spaces. Ann. Polon. Math. 121 (2018), no. 1, 91--98.  link

Pan, Jian; Zhang, Zujin; Zhou, Xiangying. Optimal dynamic mean-variance asset-liability management under the Heston model. Adv. Difference Equ. 2018, 2018:258.  link

Zhang, Zujin. Several new regularity criteria for the axisymmetric Navier-Stokes equations with swirl. Comput. Math. Appl. 76 (2018), no. 6, 1420--1426.  link

Zhang, Zujin; Tang, Tong. Global regularity for a special family of axisymmetric solutions to the three-dimensional magnetic Bénard problem. Appl. Anal. 97 (2018), no. 14, 2533--2543.   link

Zhang, Zujin; Wu, Chupeng. Some new multiplicative Sobolev inequalities with applications to the Navier-Stokes equations. Ann. Polon. Math. 121 (2018), no. 3, 279--290.  link

Zhang, Zujin. Remarks on regularity criteria for the 2D generalized MHD system in Besov spaces. Rocky Mountain J. Math. 48 (2018), no. 8, 2785--2795.   link

邱树林, 张祖锦, 刘智广, 范丽娜. 函数在多个点Taylor展开[J]. 赣南师范大学学报, 2018, 06: 13-14.  link

Tang, Tong; Zhang, Zujin. A remark on the global existence of weak solutions to the compressible quantum Navier-Stokes equations. Nonlinear Anal. Real World Appl. 45 (2019), 255--261.   link

Zhang, Zujin; Wang, Weihua; Yao, Zheng-an. Components reduction regularity results for the Navier-Stokes equations in general dimensions. J. Math. Anal. Appl. 469 (2019), no. 2, 827--840.  link

Zhang, Zujin. New a priori estimates for the axisymmetric Navier-Stokes system. Appl. Math. Lett. 92 (2019), 139--143.   link

Zhang, Zujin; Wang, Weihua; Yang, Xian. An extension and simpler proof of Berselli–C'ordoba's geometric regularity condition for the Navier–Stokes system. Comput. Math. Appl. 77 (2019), no. 3, 765--769.  link

Zhang, Zujin; Yuan, Weijun; Zhou, Yong. Some remarks on the Navier-Stokes equations with regularity in one direction. Appl. Math. 64 (2019), no. 3, 301--308.  link

谢元福, 张祖锦. 拓扑空间中子集的导集的计算[J]. 赣南师范大学学报, 2019, 03: 7-8.  link

Zhang, Zujin. Regularity Criteria for the Axisymmetric Navier–Stokes System with Negative Weights. Results Math. 74 (2019), no. 4, 74:134.  link

Zhang, Zujin; Pan, Jian; Qiu, Shulin. Extended Regularity Criteria for the Navier–Stokes–Maxwell system. Bull. Malays. Math. Sci. Soc. 42 (2019), no. 5, 2039--2046.  link

Zhang, Zujin. Remarks on the energy equality for the non-Newtonian fluids. J. Math. Anal. Appl. 480 (2019), no. 2, 123443.  link

Zhang, Zujin; Wu, Chupeng; Zhou, Yong. On Ratio Improvement of Prodi-Serrin-Ladyzhenskaya Type Regularity Criteria for the Navier-Stokes System. Czechoslovak Math. J. 69 (2019), no. 4, 1165--1175.  link

Zhang, Zujin; Wang, Weihua; Zhou, Yong. Global regularity criterion for the Navier-Stokes equations based on the direction of vorticity. Math. Methods Appl. Sci. 42 (2019), no. 18, 7126--7134.   link

张祖锦;郭雅妮;杨娴;.一类广义积分与无穷级数的条件收敛性[J].赣南师范大学学报,2019,06:11-13.  link

Zhang, Zujin; Wang, Sinan. Weighted a priori estimates for the swirl component of the vorticity of the axisymmetric Navier–Stokes system. Appl. Math. Lett. 104 (2020), 106275.  link

Zhang, Zujin; Zhang, Yali. On regularity criteria for the Navier-Stokes equations based on one directional derivative of the velocity or one diagonal entry of the velocity gradient. Z. Angew. Math. Phys. 72 (2021), no. 1, 24.  link

Zhang, Zujin; Wang, Sinan. Serrin type regularity criterion for the shear thinning fluids via the velocity field. Appl. Math. Lett. 116 (2021), 107011.  link

Fan, Jishan; Zhang, Zujin. Regularity Criteria of the Density-Dependent Incompressible Ideal Boussinesq and Liquid Crystals Model. Acta Appl. Math. 173 (2021), 3.   link

Alghamdi, Ahmad Mohammad; Gala, Sadek; Ragusa, Maria Alessandra; Zhang, Zujin. A Regularity Criterion for the 3D Density-Dependent MHD Equations. Bull. Braz. Math. Soc. (N.S.) 52 (2021), no. 2, 241--251.   link

Zhang, Zujin; Zhang, Yali. An Improved Regularity Criteria for the MHD System Based on Two Components of the Solution. Appl. Math. 66 (2021), no. 3, 451--460.  link