姜在红

博士，女，汉族，中共党员，浙江师范大学, 数学科学学院应用数学系, 教授，博导。

主讲课程

主讲本科课程：高等数学、解析几何、数学分析

主讲研究生课程：偏微分方程、双曲守恒律基础、动理学方程基础

学术兴趣及主要研究方向

物理、力学中的偏微分方程，特别是流体力学方程及动理学方程。近期的研究主要有：一些动理学模型的大扰动解的适定性、动理学方程初边值问题以及浅水波方程解的大时间性态.

科研项目

1.几类动理学方程及相应宏观模型解的性态，12071439，国家自然科学基金委面上项目，2021.01-2024.12，51万，在研，主持.

2. 流体力学-动理学耦合方程组的渐近行为，LY19A010016，浙江省自然科学基金一般项目，2019.01-2021.12，6万，在研，主持.

3. 流体力学中的非线性偏微分方程及相关领域的研究进展，S20A010004，浙江省学术交流项目，2020.03-2021.03，5万，在研主持.

4. Boltzmann方程解渐近性态的若干研究，LY15A010009，浙江省自然科学基金一般项目，2015.01-2017.12，6万，已结题，主持.

5. 两类动力学方程数学理论的一些研究，11101376， 国家自然科学基金委员会，青年科学基金项目，2012.01-2014.12，22万元，已结题，主持.

6. 几类动理学方程的解的性态研究， 11671309，国家自然科学基金委面上项目，2017.01-2020.12，48万（浙师大到账9.6万），已结题，参加.

7. 几类非典型薛定谔方程的变分方法研究，11671364，国家自然科学基金委面上项目，2017.01-2020.12，48万，已结题，参加.

8. 可压缩Navier-Stokes方程的一些研究，11171154，国家自然科学基金委员会，面上项目，2012.01-2015.12，45万元，已结题，参加.

9. 非局域作用下非线性薛定谔方程解的分类，11971436，国家自然科学基金委员会，国际合作交流项目， 2020.07-2022.06，10万元，在研，参加.

发表论文和著作

1. Zhu, Mingxuan; Jiang, Zaihong The Cauchy problem for the Camassa-Holm-Novikov equation. Acta Math. Sci. Ser. B (Engl. Ed.) 43 (2023), no. 2, 736–750.

2. Huang, Fei-min; Jiang, Zai-hong; Wang, Yong Boundary layer solution of the Boltzmann equation for specular boundary condition Acta Math. Appl. Sin. Engl. Ser. 39 (2023), no. 1, 65–94.

3. Zhu, Mingxuan; Jiang, Zaihong; Qiao, Zhijun Analytical properties for the fifth-order b-family Novikov model. J. Evol. Equ. 22 (2022), no. 1, Paper No. 19, 22 pp.

4. Zhu, Mingxuan; Jiang, Zaihong; Qiao, Zhijun Persistence property and infinite propagation speed for the  b -family of Fokas-Olver-Rosenau-Qiao ( b FORQ) model. Appl. Math. Lett. 124 (2022), Paper No. 107652, 8 pp.

5. Jiang, Zaihong; Ma, Caochuan; Zhou, Yong* Commutator estimates with fractional derivatives and local existence for the generalized MHD equations. Z. Angew. Math. Phys. 72 (2021), no. 3, Paper No. 111, 13 pp. 

6. 2. Jiang, Zaihong; Zhang, Qingning; Zhu, Mingxuan* Global existence and long time behavior of the generalized Camassa-Holm equation with k+1 degree nonlinearities. J. Math. Phys. 62 (2021), no. 5, Paper No. 051504, 11 pp. 

7.  Cao, Lu; Jiang, Zaihong*; Zhu, Mingxuan Large time behavior for the support of momentum density of the Holm-Staley b-family equation with weakly dissipative term. Nonlinear Anal. Real World Appl. 53 (2020), 103069, 12 pp.

8.  Jiang, Zaihong; Cao, Lu; Zou, Rong* Global regularity of n dimensional generalized MHD equations without magnetic diffusion. Appl. Math. Lett. 101 (2020), 106065, 7 pp. 

9.  Jiang, Zaihong; Zhu, Mingxuan* Asymptotic behavior, regularity criterion and global existence for the generalized Navier-Stokes equations. Bull. Malays. Math. Sci. Soc. 42 (2019), no. 3, 1085–1100. 

10.  Li, Li; Jiang, Zaihong*; Cai, Xinliang Solutions for stationary Navier-Stokes equations with non-homogeneous boundary conditions in symmetric domains of ℝn. J. Math. Anal. Appl. 469 (2019), no. 1, 1–15. 

11.  Jiang, Zaihong; Zhang, Shuyun; Zhu, Mingxuan* Global regularity for the Navier-Stokes-Maxwell system with fractional diffusion. Math. Phys. Anal. Geom. 21 (2018), no. 3, Paper No. 17, 13 pp. 

12.  Jiang, Zaihong*; Geng, Jinbo; Li, Li; Zhong, Ning Asymptotic stability of a fluid-particles interaction model with external forces. J. Math. Phys. 59 (2018), no. 1, 011511, 15 pp. 

13.  Jiang, Zaihong; Li, Li*; Zhong, Ning The Cauchy problem of a fluid-particle interaction model with external forces. Math. Methods Appl. Sci. 41 (2018), no. 1, 212–233. 

14.  Jiang, Zaihong; Zhu, Mingxuan* Regularity criteria for the 3D generalized MHD and Hall-MHD systems. Bull. Malays. Math. Sci. Soc. 41 (2018), no. 1, 105–122. 

15.  Ma, Caochuan; Jiang, Zaihong; Zhu, Mingxuan* Scaling invariant regularity criteria for the Navier-Stokes-Maxwell system. Appl. Math. Lett. 76 (2018), 130–134. 

16.  Ma, Caochuan; Jiang, Zaihong; Zhu, Mingxuan* Global existence and zero α limit of the 3D incompressible two-fluid MHD equations. Math. Methods Appl. Sci. 40 (2017), no. 16, 5760–5767.

17.  Jiang, Zaihong*; Liu, Baixin; Ma, Caochuan Local existence of strong solutions to the generalized Boussinesq equations. Appl. Anal. 96 (2017), no. 4, 714–720. 

18.  Ma, Caochuan; Jiang, Zaihong*; Wan, Renhui Local well-posedness for the tropical climate model with fractional velocity diffusion. Kinet. Relat. Models 9 (2016), no. 3, 551–570. 

19.  Jiang, Zaihong; Wang, Yanan; Zhou, Yong* On regularity criteria for the 2D generalized MHD system. J. Math. Fluid Mech. 18 (2016), no. 2, 331–341. 

20.  Wang, Yanan; Zhou, Yong; Alsaedi, Ahmed; Hayat, Tasawar; Jiang, Zaihong* Global regularity for the incompressible 2D generalized liquid crystal model with fractional diffusions. Appl. Math. Lett. 35 (2014), 18–23. 

21.  Jiang, Zaihong*; Wang, Ying Global existence and decay estimates of the Boltzmann equation with frictional force: the general results. J. Math. Anal. Appl. 417 (2014), no. 1, 481–503. 

22.  Jiang, Zaihong*; Fan, Jishan Time decay rate for two 3D magnetohydrodynamics-α models. Math. Methods Appl. Sci. 37 (2014), no. 6, 838–845. 

23.  Jin, Yanyi; Jiang, Zaihong* Wave breaking of an integrable Camassa-Holm system with two components. Nonlinear Anal. 95 (2014), 107–116. 

24.  Jiang, Zaihong; Zhou, Yong*; Zhu, Mingxuan Large time behavior for the support of momentum density of the Camassa-Holm equation. J. Math. Phys. 54 (2013), no. 8, 081503, 7 pp.

25.  Jia, Xuanji; Jiang, Zaihong* An anisotropic regularity criterion for the 3D Navier-Stokes equations. Commun. Pure Appl. Anal. 12 (2013), no. 3, 1299–1306. 

26.  Jiang, Zaihong* Asymptotic behavior of strong solutions to the 3D Navier-Stokes equations with a nonlinear damping term. Nonlinear Anal. 75 (2012), no. 13, 5002–5009. 

27.  Jiang, Zaihong; Ni, Lidiao; Zhou, Yong* Wave breaking of the Camassa-Holm equation. J. Nonlinear Sci. 22 (2012), no. 2, 235–245.

28.  Jiang, Zaihong; Zhu, Mingxuan The large time behavior of solutions to 3D Navier-Stokes equations with nonlinear damping. Math. Methods Appl. Sci. 35 (2012), no. 1, 97–102.

29.  Wang, Ying; Jiang, Zaihong* The specular reflective boundary problem for the Boltzmann equation with soft potentials. Nonlinear Anal. 75 (2012), no. 2, 786–805. 

30.  Zhu, Mingxuan; Jiang, Zaihong Some properties of solutions to the weakly dissipative b-family equation. Nonlinear Anal. Real World Appl. 13 (2012), no. 1, 158–167. 

31.  Jiang, Zaihong*; Ni, Lidiao Blow-up phenomenon for the integrable Novikov equation. J. Math. Anal. Appl. 385 (2012), no. 1, 551–558. 

32.  Jiang, Zaihong*; Fan, Jishan Vanishing heat conductivity limit for the 2D Cahn-Hilliard-Boussinesq system. Bound. Value Probl. 2011, 2011:54, 6 pp. 

33.  Jiang, Zaihong*; Gala, Sadek; Ni, Lidiao On the regularity criterion for the solutions of 3D Navier-Stokes equations in weak multiplier spaces. Math. Methods Appl. Sci. 34 (2011), no. 16, 2060–2064. 35Q30 (35B65)

34.  Liu, Xuefei; Zhu, Mingxuan; Jiang, Zaihong* On the Cauchy problem for the b-family equations with a strong dispersive term. J. Appl. Math. 2011, Art. ID 513467, 15 pp. 

35.  Jiang, Zaihong; Wang, Ying Decay estimation in nonlinear hyperbolic system of conservation laws. J. Math. Anal. Appl. 377 (2011), no. 2, 863–873. 

36.  Ying, Wang; Jiang, Zaihong* Optimal time decay of the Boltzmann equation with frictional force. J. Math. Anal. Appl. 374 (2011), no. 2, 499–515. 

37.  Hua, Jiale*; Jiang, Zaihong; Yang, Tong A new Glimm functional and convergence rate of Glimm scheme for general systems of hyperbolic conservation laws. Arch. Ration. Mech. Anal. 196 (2010), no. 2, 433–454. 

38.  Hua, Jiale; Jiang, Zaihong* Decay estimate for a new measure of rarefaction waves in general systems of conservation laws. J. Differential Equations 247 (2009), no. 11, 3100–3116. 

39.  Jiang, Zaihong; Yang, Tong* A new nonlinear functional for general scalar conservation laws. J. Differential Equations 246 (2009), no. 11, 4284–4308. 

科研获奖