张映辉


博士，教授，博士生导师，广西****基金获得者，广西高等学校中青年骨干教师，广西师范大学A类漓江****。
Email:zhangyinghui0910@126.com

流体力学及生物学中的偏微分方程、数学教育


1.本科生课程：《数学分析》、《常微分方程》等
2.研究生课程：《Sobolev空间》、《现代偏微分方程》等


[1]国家自然科学基金青年项目:两类非线性双曲-抛物耦合方程的粘性消失极限问题（**），已结题。
[2]国家自然科学基金天元青年基金项目:非等熵可压缩Navier-Stokes方程的零耗散极限问题（**），已结题。
[3]广西****科学基金项目：偏微分方程（2019JJG10003），在研。
[4]广西科技计划人才专项项目：具有磁场效应的两相流模型的衰减率研究(2019AC20214）,在研。
[5]国家自然科学基金面上项目子项目：可压缩Navier-Stokes-Vlasov-Fokker-Pl
-anck方程及相关模型解的适定性（**），在研。
[6]国家自然科学基金面上项目子项目：可压缩非守恒两相流模型的若干数学问题（**），在研。
[7]湖南省自然科学基金面上项目：液体-气体两相流模型初边值问题的研究（2017JJ2105），已结题。
[8]湖南省自然科学基金青年项目：Navier-Stokes方程的零耗散极限问题研究（13JJ4095），已结题。
[9]中国博士后科学基金：可压Navier-Stokes方程的粘性消失极限问题研究（2012M511640），已结题。
[10]湖南省教育厅优秀青年项目：两类非线性偏微分方程初值问题的适定性和零耗散极限（14B077），已结题（鉴定为优秀）。
[11]湖南省教育厅一般项目：Navier-Stokes方程的消失的粘性极限问题（11C0628），已结题。

专著
[1]Yinghui Zhang*,Zhong Tan, MathematicalanalysisofNavier-Stokes equations and related models,LAP Lambert Academic Publishing，Germany, 2014.
论文
[1]Guochun Wu,Yinghui Zhang*,LanZou,Optimallargetimebehaviorofthetwo-phasefluidmodelinthewholespace,SIAMJournalonMathematicalAnalysis,52(6)(2020),5748-5774.
[2]Guochun Wu, Yinghui Zhang*, Weiyuan Zou, Optimal time-decay rates forthe 3D compressible Magnetohydrodynamic flows with discontinuous initial dataand large oscillations, Journal of the London Mathematical Society, doi: 10.1112/jlms.12393, 2020.
[3]Yinghui Zhang*, Local well-posedness ofthe free-surface incompressible elastodynamics, Journal of Differential Equations, 268 (2020), 6971–7011.
[4] Guochun Wu, YinghuiZhang*, Global well-posedness and large time behavior of the viscousliquid-gas two-phase flow model in R^3, Proceedings of the Royal Society of Edinburgh Section A Mathematics, 150 (2020), 1999–2024.
[5] Guochun Wu, Yinghui Zhang*, Anzhen Zhang. Global existenceand time decay rates for the 3D bipolar compressible Navier-Stokes-Poissonsystem with unequal viscosities,Science China Mathematics, doi.org/10.1007/s11425-020-1719-9, 2020.
[6] Yinghui Zhang*,Weaksolutions for an inviscid two-phase flow model in physical vacuum, Journal of Differential Equations,265（12）(2018), 6251–6294.
[7] Yinghui Zhang,Changjiang Zhu, Global existence and optimal convergence rates for the strongsolutions in to the 3D viscous liquid-gastwo-phase ?ow model, Journal of Differential Equations, 258 (7) (2015), 2315–2338.
[8] Yinghui Zhang*,Ronghua Pan, Yi Wang, Zhong Tan, Zero dissipation limit with two interactingshocks of the 1D non-isentropic Navier-Stokes equations, Indiana University Mathematics Journal, 62(1)2013,249–309.
[9] Yinghui Zhang*,Decay of the 3D inviscid liquid–gas two-phase ?ow model, Zeitschriftfür angewandte Mathematik und Physik, 67 (54) (2016), 1–22.
[10] Yinghui Zhang*,Decay of the 3D viscous liquid-gas two-phase ?ow model with damping,Journal of Mathematical Physics , 081517, 2016.
[11] Guochun Wu, YinghuiZhang*,Global analysis of strong solutions for the viscous liquid-gastwo-phase flow model in a bounded domain, Discrete and Continuous Dynamical System – B, 23(4) (2018), 1411–1429.
[12] YinghuiZhang*, Ronghua Pan, Zhong Tan, Zero dissipation limit to a Riemannsolution consisting of two shock waves for the 1D compressible isentropicNavier-Stokes equations, Science China Mathematics, 56(11)2013, 2205–2232.
[13]QingChen, Guochun Wu, Yinghui Zhang*, LanZou, Optimal timedecay rates for the compressible Navier-Stokes system with and withoutYukawa-type potential. Electronic Journal of Differential Equations (2020), 2020(102): 1-25.
[14] YinghuiZhang*, Zhong Tan, Ming-Bao Sun,Global existence and asymptotic behavior of smoothsolutions to a coupled hyperbolic-parabolic system, Nonlinear Analysis: Real World Applications, 14(2013), 465–482.
[15] Yinghui Zhang*,Zhong Tan, Ming-Bao Sun, Zero relaxation limit to centered rarefactionwaves for Jin-Xin relaxation system,Nonlinear Analysis: Theory, Methods & Applications,74(2011),2249–2261.
[16] Yinghui Zhang*,Zhong Tan, Existence and asymptotic behavior of global smooth solution forp-System with damping and boundary effect, Nonlinear Analysis:Theory, Methods & Applications,72(2010),2499–2513.
[17] Yinghui Zhang*, Zhong Tan, On theexistence of solutions to the Navier-Stokes-Poissonequations of a two-dimensional compressibleflow, Mathematical Methods in the Applied Sciences, (30)(2007), 305–329.
[18] Yinghui Zhang*, Initial boundary value problem for the 3D quasilinearhyperbolic equations with nonlinear damping,Applicable Analysis, 98(11)(2019), 2048–2063.
[19] Yinghui Zhang*,Zhong Tan, Blow-up of smooth solutions to the compressible fluid models ofKorteweg type, Acta Mathematica Sinica, English Series, 28(3)2012, 645–652.
[20] Yinghui Zhang*,Zhong Tan, Asymptotic behavior of solutions to the Navier-Stokes equationsof a two-dimensional compressible flow, Acta Mathematicae Applicatae Sinica, English Series, 27(4)2011, 697–712.
[21] Yinghui Zhang*, Haiying Deng, Ming-Bao Sun, Global analysis of smooth solutions to a hyperbolic-parabolic coupled system, Frontiers of Mathematics in China, 8(6)2013, 1437–1460.
[22] Lianhong Guo, Yinghui Zhang*, The 3D quasilinear hyperbolic equations with nonlinear damping in a general unbounded domain, Annales Polonici Mathematici, 121.2(2018),133–155.
[23] Yinghui Zhang*, Guochun Wu, Global existence and asymptotic behavior for the 3D compressible non-isentropic Euler equations with damping, Acta Mathematica Scientia,34B(2)(2014), 424–434.
[24] Yinghui Zhang*, Guochun Wu, The 3D Non-isentropic Compressible Euler Equations with Damping in a Bounded Domain, Chinese Annals of Mathematics, Series B, 37(6)(2016): 915–928.
[25] Zhong Tan, YinghuiZhang*, Shape optimization in two-dimensional viscous compressible fluids, Acta Mathematica Sinica, EnglishSeries, 26(9)2010, 1793–1806.
[26] Zhong Tan, YinghuiZhang*,Strong solutions of the coupled Navier-Stokes-Poisson equations forisentropic compressible fluids,Acta Mathematica Scientia, 30B(4)(2010), 1280–1290.
[27] Mina Jiang, YinghuiZhang*, Existence and asymptotic behavior of global smooth solution forp-system with nonlinear damping and fixed boundary effect,Mathematical Methods in the Applied Sciences,37(2014), 2585–2596.
[28] Yinghui Zhang*,Zhong Tan, Baishun Lai, Ming-Bao Sun, Global analysis ofsmooth solutions to a generalized hyperbolic-parabolic system modelingChemotaxis, ChineseAnnals of Mathematics, 33A(1)2012, 27-38;transl.in ChineseJournal of Contemporary Mathematics, 33(1)2012, 17–28.
[29] Yinghui Zhang*, Zhong Tan, Ming-Bao Sun, Global SmoothSolutions to a Coupled Hyperbolic-Parabolic System,Chinese Annals of Mathematics,34A(1)2013, 29-46; transl. in Chinese Journal ofContemporary Mathematics, 34(1)2013, 19–36.

[1]成果“次黎曼流形上的分析和非线性偏微分方程若干问题的研究”获湖南省自然科学奖三等奖（2/2），2017年。
[2]成果“两类流体力学方程的适定性和零耗散极限”获岳阳市科学技术进步奖二等奖(1/2)，2016年。
[3]获得广西****基金，2019年。
[4]入选广西高等学校中青年骨干教师，2019年。
[5]入选广西师范大学A类漓江****，2019年。
[6]获得湖南省普通高校教学竞赛二等奖，2011年。


美国《数学评论》(Mathematical Reviews)评论员、
国际期刊《SCIREA Journal of Mathematics》编委





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