教师简介

首页 > 教师简介
个人信息
  • 姓名:郭真华
  • 部门:应用数学系
  • 职称:教授
  • 荣誉:博士生导师,专业学位硕士生导师
  • 电子邮件:
  • 研究方向:流体力学方程、非线性偏微分方程。

 

个人简介

 

 

    郭真华,湖北孝感人,教授,博士生导师。生于1970年10月。1993年4月入党。1994、1997年毕业于华中师范大学,并获理学学士学位和硕士学位,2003年毕业于香港中文大学数学科学研究所,获哲学博士学位。2004年至2005年在北京应用物理与计算数学研究所从事博士后研究。现任西北大学数学学院院长,陕西省流体力学数学理论与计算重点实验室主任(兼)、《纯粹数学与应用数学》常务副主编、陕西省数学竞赛委员会办公室主任。主要学术兼职有:中国数学会理事,中国工业与应用数学会理事;陕西省数学会常务理事,陕西省工业与应用数学会常务理事、副理事长,美国数学会评论员,国际期刊《International Journal of Partial Differential Equations》编委。国家自然科学基金委、国家留学基金委以及教育部博士后基金项目评审专家,国家科学技术奖评审专家等。

 

 

项目、成果、论文、奖励

 

  •  

  • 1.主要课题

     

    1.国家自然科学基金重点项目(11931013):石油开发中多相流体相互作用的建模、数学理论与数值模拟。直接经费:270万元人民币,2020年1月至2024年12月, 项目主持人;

    2.国家自然科学基金面上项目(11671319):流体力学方程组中若干问题的研究。直接费用:48万元人民币,2017年1月至2020年12月, 项目主持人;  

    3.国家自然科学基金重点项目(11331005):流体力学方程的数学理论。经费:240万元人民币,2014年1月至2018年12月, 排名第三,子项目主持人( 经费98万);

    4.国家自然科学基金天元基金项目(11726020):第十五届非线性偏微分方程暑期讲习班暨学术会议。经费:18万元人民币,2017年4月至2017年10月, 项目主持人;

    5.教育部博士点基金 (20136101110015):可压Navier-Stokes方程的数学理论。经费:12万元人民币,2014年1月至2016年12月,项目主持人;

    6.国家自然科学基金面上项目(11071195):流体力学中的自由边值问题。经费:29万元人民币,2011年1月至2013年12月, 项目主持人;

    7.国家自然科学基金天元基金项目(11226001):中国数学会 2012 年学术年会。经费:10万元人民币,2012年8月至2012年12月, 项目主持人;

    8.国家自然科学基金面上项目(10771170):高维可压Navier-Stokes方程的真空问题。经费:24万元人民币,2008年1月至2010年12月, 项目主持人;

    9.国家自然科学基金青年基金项目(10401012):可压Navier-Stokes方程解的长时间行为。经费:11万元人民币,2005年1月至2007年12月,项目主持人;

    10.教育部留学回国人员科研启动金 (教外司留2004[176]):可压Navier-Stokes方程的自模解及解的长时间行为。经费:2.5万元人民币,2004年12月至2006年12月,项目主持人。

  •  

  •  

    2.主要成果    

     

    1.Guo, Zhenhua; Dong, Wenchao; Liu, Jinjing Large-time behavior of solution to an inflow problem on the half space for a class of compressible non-Newtonian fluids. Commun. Pure Appl. Anal. 18 (2019), no. 4, 2133–2161.

    2.Guo, Zhenhua; Song, Wenjing, Global well-posedness and large-time behavior of classical solutions to the 3D Navier-Stokes system with changed viscosities. J. Math. Phys. 60 (2019), no. 3, 031502, 29 pp.

    3.Bianru Cheng, Zhenhua Guo, Dongling Wang,Dissipativity of semilinear time fractional subdiffusion equations and numerical approximations ,Applied Mathematics Letters 86 (2018) 276–283

    4.Li Fang, Huan Zhu, Zhenhua Guo,Global classical solution to a one-dimensional compressible non-Newtonian fluid with large initial data and vacuum ,Nonlinear Analysis 174 (2018) 189–208

    5.Guo Zhenhua, Wang Mei, Wang Yi; Global solution to 3D spherically symmetric compressible Navier-Stokes equations with large data. Nonlinear Analysis: Real World Applications 40 (2018) 260–289

    6.Zilai Li, Zhenhua Guo, On Free Boundary Problem For Compressible Navier-Stokes Equations With Temperature-Dependent Heat Conductivity , Discrete And Continuous Dynamical Systems Series B , Volume 22, Number 10, December 2017, doi: 10. 3934/dcdsb. 2017201. pp. 3903-3919

    7.Mei Wang, Zilai Li, Zhenhua Guo; Global weak solution to 3D compressible flows with density-dependent viscosity and free boundary. Commun. Pure Appl. Anal. 16 (2017), no. 1, 1–23.

    8.Fang, Li; Guo, Zhenhua; Zero dissipation limit to rarefaction wave with vacuum for a one-dimensional compressible non-Newtonian fluid. Commun. Pure Appl. Anal. 16 (2017), no. 1, 209–242.

    9.Su, Wenhuo; Guo, Zhenhua; Yang, Ganshan Global solution of 3D axially symmetric nonhomogeneous incompressible MHD equations. J. Differential Equations 263 (2017), no. 12, 8032–8073.

    10.L. Fang, Z. H. Guo, Global well-posedness of strong solutions to the two-dimensional barotropic compressible Navier–Stokes equations with vacuum, Zeitschrift fur Angewandte Mathematik und Physik, vol. 67, no. 2, 2016.

    11.L. Fang, Z. H. Guo, Y.X. Wang, Local strong solutions to a compressible non-Newtonian fluid with density-dependent viscosity, Mathematical Methods in the Applied Sciences, 2016, 2(4):258-258 .

    12.Mei Wang, Zilai Li, Zhenhua Guo, Global Weak Solution to 3D Compressible Flows with Density-dependent Viscosity and 
Free Boundary, Comm. On Pure and Applied Analysis. , Volume 15, Number 2, March 2016, doi: 10. 3934/cpaa. 2016. 15.

    13.Zhenhua Guo, Zilai Li, Global existence of weak solution to the free boundary problem for compressible Navier-Stokes, Kinetic and Related Models, 9 (2016), no. 1, 75–103.

    14.Lu, Yang; Fei, Liang; Zhenhua,  GuoLower bounds for blow-up time of a nonlinear viscoelastic wave equation. Bound. Value Probl. 2015, 2015:219, 6 pp. 35L72

    15.Yao, Lei; Yang, Jing; Guo, Zhen-hua Global classical solution for a three-dimensional viscous liquid-gas two-fluid flow model with vacuum. Acta Math. Appl. Sin. Engl. Ser. 30 (2014), no. 4, 989–1006.

    16.Liang, Fei; Guo, Zhenhua Asymptotic behavior for second order stochastic evolution equations with memory. J. Math. Anal. Appl. 419 (2014), no. 2, 1333–1350.

    17.Wei, Jin-tao; He, Lin; Guo, Zhen-hua A remark on the Cauchy problem of 1D compressible Navier-Stokes equations with density-dependent viscosity coefficients. Acta Math. Appl. Sin. Engl. Ser. 30 (2014), no. 1, 193–204.

    18.Gao, Wen; Guo, Zhen-hua; Niu, Dong-juan Global helically symmetric solutions to 3D MHD equations. Acta Math. Appl. Sin. Engl. Ser. 30 (2014), no. 2, 347–358.

    19.Guo, Zhenhua; Li, Zilai; Yao, Lei Existence of global weak solution for a reduced gravity two and a half layer model. J. Math. Phys. 54 (2013), no. 12, 121503, 19 pp.

    20.Zhenhua Guo,  Zhouping Xin, Analytical solutions to the compressible Navier–Stokes equations with density-dependent viscosity coefficients and free boundaries, Journal of  Differential Equations,253 (2012) 1–19

    21.Zhenhua Guo, Hai-Liang Li, Zhouping Xin,Lagrange Structure and Dynamics for Solutions to the Spherically Symmetric Compressible Navier-Stokes Equations,Commun.  Math. Phys.,309(2012), 371-412

    22.Zhenhua Guo, Quansen. Jiu,  Zhouping Xin,Spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients. SIAM  J. MATH. ANAL. Vol.39, No.5(2008)1402-1427

    23.Z.H. Guo, C.J. Zhu, Remarks On One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum,  Acta Mathematica Sinica, English Series, (2010)26,No.10, 2015-2030

    24.Z.H. Guo, C.J. Zhu, Global Weak Solutions and Asymptotic Behavior to 1D Compressible Navier-Stokes Equations with Density-Dependet Viscosity and Vacuum,  J. Diff. Eqn., 248( 2010), 2768-2799

    25.Zhenhua Guo, Mina Jiang, Zhi'an Wang and Gaofeng Zheng, Global weak solutions to the Camassa-Holm equation. Discrete and Continuous Dynamical Systems. Vol.21, No.3(2008)883-906

    26.Zhenhua Guo, Song Jiang, Feng Xie,Global Existence and Asymptotic Behavior of Weak Solutions to the 1D Compressible Navier-Stokes Equations with Degenerate Viscosity Coefficient. Asymptotic Analysis 60(2008)101-123

    27.Zhenhua Guo,Song Jiang,  Self-similar Solutions to the Isothermal Compressible Navier-StokesEquations。IMA Journal of Applied Mathematics, (2006)71, 658-669

    28.Zhenhua Guo, Jing Yang, and Lei Yao,Global strong solution for a three-dimensional viscous liquid-gas two-phase flow model with vacuum,J. Math. Phys. 52, 093102 (2011); doi: 10.1063/1.3638039

    29.Z.H. Guo, Wen He, Interface Behavior of Compressible Navier-Stokes with Discontinuous Boundary Conditions and Vacuum, Acta Mathematica Scientia, 2011, 31B(3), 934-952

    30.Zhenhua Guo, Zilai Li, and Lei Yao, Existence of global weak solution for a reduced gravity two and a half layer model, Journal of Mathematical Physics 54, 121503 (2013); doi: 10.1063/1.4836775(SCI)

    31.Zhenhua Guo,Large-time Behavior of Solutions to the Stokes Approximation Equations for Two Dimensional Compressible Flows. Acta Mathematicae Applicatae Sinica,English Series, Vol.21, No.4 (2005) 1-18

    32.Zhenhua Guo,Song Jiang and Jing Li,  Global Helically Symmetric Solutions to the Stokes Approximation Equations for Three-Dimensional Compressible Viscous Flows。MAA Methods and Applications of Analysis,Vol.12, No.2, pp.135-152, June 2005

    33.Li Fang, Zhenhua Guo*, Analytical solutions to a class of non-Newtonian fluids with free boundaries, J. Math. Phys. 53, 103701 (2012); doi: 10.1063/1.4748523

    34.Ruxu Lian, Zhenhua Guo, Hai-Liang Li, Dynamical behaviors for 1D compressible Navier–Stokes equations with density-dependent viscosity.  Journal of  Differential Equations,248(2010) ,1926-1954

    35.Wenjun  Sun,Song  Jiang and Zhenhua  Guo, Helically Symmetric Solutions to the 3-D Navier-Stokes Equations for Compressible Isentropic Fluids. Journal of Differential Equations,  222(2006) 263-296

    36.Yinbing Deng, Zhenhua Guo and Gengsheng Wang, Nodal solutions for $p$-Laplace equations with critical growth,Nonlinear Anal. 54(2003), no.6, 1121-1151

    37.Gao, Wen; Guo, Zhen-hua; Niu, Dong-juan; Global helically symmetric solutions to 3D MHD equations. Acta Math. Appl. Sin. Engl. Ser. 30 (2014), no. 2, 347–358.

    38. Yao, Lei; Yang, Jing; Guo, Zhenhua, Blow-up criterion for 3D viscous liquid-gas two-phase flow model. J. Math. Anal. Appl. 395 (2012), no. 1, 175–190

    39.Lei Yao, Huiling Guo, Zhenhua Guo, A note on viscous liquid–gas two-phase flow model with mass-dependent viscosity and vacuum,Nonlinear Analysis: Real World Applications 13 (2012) 2323–2342

    40.Jintao Wei, Lin He and Zhenhua Guo, A Remark on the Cauchy Problem of 1D Compressible Navier-Stokes Equations with Density-dependent Viscosity coefficients.  Acta Math. Appl. Sin. Engl. Ser. 30 (2014), no. 1, 193–204.

    41.L. Fang, Z. H. Guo, Global well-posedness of strong solutions to the two-dimensional barotropic compressible Navier–Stokes equations with vacuum, Zeitschrift fur Angewandte Mathematik und Physik, vol. 67, no. 2, 2016.

    42.L. Fang, Z. H. Guo, Y.X. Wang, Local strong solutions to a compressible non-Newtonian fluid with density-dependent viscosity, Mathematical Methods in the Applied Sciences, 2016, In Press.

    43.Mei Wang, Zilai Li, Zhenhua Guo, Global Weak Solution to 3D Compressible Flows with Density-dependent Viscosity and 
Free Boundary, Comm. On Pure and Applied Analysis. , Volume 15, Number 2, March 2016, doi: 10. 3934/cpaa. 2016. 15.

    44.Lu Yang, Fei Liang, Zhenhua Guo, Lower bounds for blow-up time of a nonlinear viscoelastic wave equation, Boundary Value Problems (2015) 2015:219,6pp, DOI 10.1186/s13661-015-0479-1

  •  

  •  

    3.获奖情况    

     

    1.《流体力学若干方程组的数学理论》,陕西省科学技术奖二等奖,2014年,第一完成人;

    2.《流体力学若干方程组的研究》, 陕西高等学校科学技术奖二等奖(12A19),2012年,第一完成人;

    3.“ 数理统计及金融数学教学团队建设”教学团队,西北大学,主持人,2012年;

    4.“ 数理统计及金融数学教学团队建设”省级教学团队,陕西省教育厅,主持人,2012年

    5.《面向信息时代的常微分方程》2001年获湖北省人民政府省级教学成果一等奖 (排名第五);

    6.《数学拔尖创新人才培养体系建设》2011年获西北大学教学成果奖一等奖(排名第三);

    7.《常微分方程课程教学模式创新与实践》2011年获西北大学教学成果奖二等奖(排名第二);

    8.《地方综合性大学数学拔尖创新人才培养体系的探索与实践》,陕西省教学成果奖一等奖(SJX131020-3),陕西省人民政府,2013年,第三完成人。

  •