數學與統計學院教師簡介——張映輝

張映輝     

博士，教授，博士生導師，廣西杰出青年基金獲得者，廣西高等學校中青年骨干教師，廣西師范大學A類漓江學者。

Email: zhangyinghui0910@126.com

流體力學及生物學中的偏微分方程、數學教育

1.本科生課程：《數學分析》、《常微分方程》等

2.研究生課程：《Sobolev空間》、《現代偏微分方程》等

[1]國家自然科學基金青年項目:兩類非線性雙曲-拋物耦合方程的粘性消失極限問題（11301172），已結題。

[2]國家自然科學基金天元青年基金項目:非等熵可壓縮Navier-Stokes方程的零耗散極限問題（11226170），已結題。

[3]廣西杰出青年科學基金項目：偏微分方程（2019JJG10003），在研。

[4]廣西科技計劃人才專項項目：具有磁場效應的兩相流模型的衰減率研究(2019AC20214）,在研。

[5]國家自然科學基金面上項目子項目：可壓縮Navier-Stokes-Vlasov-Fokker-Pl

-anck方程及相關模型解的適定性（11771150），在研。

[6]國家自然科學基金面上項目子項目：可壓縮非守恒兩相流模型的若干數學問題（11571280），在研。

[7]湖南省自然科學基金面上項目：液體-氣體兩相流模型初邊值問題的研究（2017JJ2105），已結題。

[8]湖南省自然科學基金青年項目：Navier-Stokes方程的零耗散極限問題研究（13JJ4095），已結題。

[9]中國博士后科學基金：可壓Navier-Stokes方程的粘性消失極限問題研究（2012M511640），已結題。

[10]湖南省教育廳優秀青年項目：兩類非線性偏微分方程初值問題的適定性和零耗散極限（14B077），已結題（鑒定為優秀）。

[11]湖南省教育廳一般項目：Navier-Stokes方程的消失的粘性極限問題（11C0628），已結題。

 



專著

[1]Yinghui Zhang*, Zhong Tan, Mathematical analysis of Navier-Stokes equations and related models, LAP Lambert Academic Publishing，Germany, 2014.

論文

[1]Guochun Wu,Yinghui Zhang*,Lan Zou, Optimal large time behavior of the two-phase fluid model in the whole space, SIAM Journal on Mathematical Analysis, 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線性偏微分方程若干問題的研究”獲湖南省自然科學獎三等獎（2/2），2017年。

[2] 成果“兩類流體力學方程的適定性和零耗散極限”獲岳陽市科學技術進步獎二等獎 (1/2)，2016年。

[3] 獲得廣西杰出青年基金，2019年。

[4] 入選廣西高等學校中青年骨干教師，2019年。

[5] 入選廣西師范大學A類漓江學者，2019年。

[6] 獲得湖南省普通高校教學競賽二等獎，2011年。

  







美國《數學評論》(Mathematical Reviews)評論員、

國際期刊《SCIREA Journal of Mathematics》編委





 

 

 

 

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