赵继红

　　 　　

 

　　一、个人简介

　　基本信息

　　赵继红，男，1982年生，理学博士，现任教于西北农林科技大学理学院，副教授。目前主要从事流体力学中偏微分方程理论和应用研究以及肿瘤生长自由边界问题的研究。

　　教育经历

　　2008/09 - 2011/06，中山大学，基础数学，博士，导师：崔尚斌教授

　　2004/09 - 2007/06，兰州大学，基础数学，硕士，导师：赵培浩教授

　　2000/09 - 2004/06，天水师范学院，数学与应用数学，学士

　　工作经历

　　2011/07- 至今，西北农林科技大学，理学院应用数学系

　　2007/07 - 2008/07，广西师范大学，数学科学学院

　　二、科研课题

　　1、国家自然科学基金青年基金，电流体动力学模型和液晶流体动力学模型大初值问题的整体适定性，项目批准号: 11501453，21.28万，2016/01-2018/12，主持。

　　2、陕西省自然科学基础研究计划—青年人才项目，一类电流体力学方程组大初值问题的整体适定性，项目批准号: 2015JQ1004，2万，2015/01-2016/12，主持。

　　3、西北农林科技大学中央高校基本科研业务费专项基金，一类电流体动力学方程组的定性分析，项目批准号: 2014YB031，10万，2014/01-2016/12，主持。

　　4、西北农林科技大学博士科研启动基金兼陕西省专项配套基金，向列型液晶流模型中若干问题的研究，项目批准号: Z109021118,  10万，2012/01-2014/12, 主持。

　　5、国家自然科学基金青年基金，基于粘性解的随机时滞方程最优控制问题研究，项目批准号: 11401474，23万，2015/01-2017/12，参加。

　　6、国家自然科学基金面上项目，一些q-特殊函数的研究，项目批准号: 11371294，56万，2014/01-2017/12，参加。

　　7、国家自然科学基金面上项目，生物学和物理学中的一些偏微分方程问题，项目批准号: 11171357，50万，2012/01-2015/12，参加。

　　8、国家自然科学基金青年基金，非自治耗散发展方程的一致吸引子, 项目批准号: 11001279, 18万，2011.01-2013.12， 参加。

　　三、研究领域

　　研究方向为偏微分方程和生物数学，目前研究兴趣集中在：流体力学中的偏微分方程组的整体适定性问题，弱解的正则性和唯一性问题，强解的衰减估计和长时间性态；Navier-Stokes方程；肿瘤生长自由边界问题；药物趋化模型的数学分析。

　　四、开设课程

　　本科生课程：数学分析；高等数学；概率论与数理统计。

　　研究生课程：泛函分析；偏微分方程；变分法；算子半群。

　　五、主要科研成果与学术论文

　　1.Well-posedness and Gevrey analyticity of the generalized Keller-Segel system in critical Besov spaces, arXiv:1508.00117.

　　2.Well-posedness and decay for the dissipative system modeling electro-hydrodynamics in negative Besov spaces,  (2017) , J. Differential Equations ,. (with Dr. Qiao Liu)

　　3.BKM's criterion for the 3D nematic liquid crystal flows via two velocity components and molecular orientations, appear in Mathematical Methods in the Applied Sciences.

　　4.Gevrey regularity of mild solutions to the parabolic-elliptic system of drift-diffusion type in critical Besov spaces， J. Math. Anal. Appl., 448 (2017), 1265-1280.

　　5.The optimal temporal decay estimates for the fractional power dissipative equation in negative Besov spaces, J. Math. Phys.,  57 (2016), 051504.

　　6.Temporal decay for the generalized Navier-Stokes equations, Nonlinear Anal. TMA. ，141 (2016) 191-210.  (with Dr. Lifei Zheng)

　　7.Blow-up criteria for the three dimensional nonlinear dissipative system modeling electro-hydrodynamics, Nonlinear Anal. RWA. ，31 (2016), 210-226.  (with Dr. Meng Bai)

　　8.Well-posedness for the 3D incompressible nematic liquid crystal system in the critical L^p  framework, Discrete Contin. Dyn. Syst. A , 36(1) (2016), 371-402. (with Dr. Qiao Liu and Prof. Ting Zhang)

　　9.On decay estimates of the 3D nematic liquid crystal flows in critical Besov spaces， Math. Meth. Appl. Sci. ， 39 (2016), 4044-4055. (with Dr. Qiao Liu)

　　10.A logarithmically improved blow-up criterion for a simplified Ericksen-Leslie system modeling the liquid crystal flows, J. Partial Differential Equations, 28(4) (2015), 358-369. (with Dr. Meng Bai and Dr. Qiao Liu)

　　11.A Beale-Kato-Majda blow-up criterion for a hydrodynamic system modeling vesicle and fluid interactions, Nonlinear Anal. TMA, 128 (2015), 20–35.

　　12.On the Serrin's regularity criterion for the beta-generalized dissipative surface quasi-geostrophic equation, Chinese Anna ls of Mathematics , Series B , 36B(6) (2015), 947-956. (with Dr. Qiao Liu)

　　13.Logarithmically improved blow-up criterion for the nematic liquid crystal system with zero viscosity, Annali di Matematica , 194 (2015), 1245–1258. (with Dr. Qiao Liu and Dr. Yining Li)

　　14.Global well-posedness for the dissipative system modeling electro-hydrodynamics with large vertical velocity component in critical Besov space, Discrete Contin. Dyn. Syst. A , 35(1) (2015), 555–582. (with Prof. Ting Zhang and Dr. Qiao Liu)

　　15.Global solutions to the 3D incompressible nematic liquid crystal system, J. Differential Equations , 258 (2015) , 1519–1547. (with Dr. Qiao Liu and Prof. Ting Zhang) 

　　16.Existence and regularizing rate estimates of mild solutions to a generalized magneto-hydrodynamic system in Q -spaces. Asian-Eur. J. Math. 8(3) (2015), 1550049. (with Dr. Qiao Liu and Prof. Shangbin Cui)

　　17.On the Cauchy problem for the fractional drift-diffusion system in critical Besov spaces, Applicable Analysis , 93(7) (2014), 1431–1450. (with Dr. Qiao Liu)

　　18.On the uniqueness of weak solutions for the 3D phase field Navier-Stokes vesicle-fluid interaction model, Diff. Equa. Appl. , 6 (1) (2014), 81–97. (with Dr. Qiao Liu and Dr. Shuanghu Zhang)

　　19.Logarithmically improved blow-up criteria for the nematic liquid crystal flows, Nonlinear Anal. RWA. , 16 (2014), 178–190. (with Dr. Qiao Liu)

　　20.Logarithmically improved regularity criterion for the 3D generalized magneto-hydrodynamic equations, Acta Mathematica Scientia , 34B(2) (2014), 1–8. (with Dr. Qiao Liu)

　　21.Global well-posedness for the generalized magneto-hydrodynamic equations in the critical Fourier–Herz spaces, J. Math. Anal. Appl. , 420 (2014), 1301–1315. (with Dr. Qiao Liu)

　　22.Uniqueness of weak solution to the generalized magneto-hydrodynamic system, Annali di Matematica , 193(3) (2014), 699-722. (with Dr. Qiao Liu)

　　23.Weak-strong uniqueness criterion for the /beta-generalized surface quasi-geostrophic equation, Monatsh Math. , 172 (2013), 431–440. (with Dr. Qiao Liu)

　　24.Logarithmically improved blow-up criteria for a phase field Navier-Stokes vesicle-fluid interaction model, J. Math. Anal. Appl. , 405 (2013), 422–437. (with Dr. Qiao Liu)

　　25.A regularity criterion for the solution of the nematic liquid crystal flows in terms of Besov-norm, J. Math. Anal. Appl. , 407 (2013), 557–566. (with Dr. Qiao Liu)

　　26.Existence of solutions for the Debye-Huckel system with low regularity initial data, Acta Applicanda Mathematicae , 125 (2013), 1–10. (with Dr. Qiao Liu and Prof. Shangbin Cui)

　　27.Global existence and stability for a hydrodynamic system in the nematic liquid crystal flows, Comm. Pure Appl. Anal. , 12(1) (2013), 341–357. (with Dr. Qiao Liu and Prof. Shangbin Cui)

　　28.Regularizing and decay rate estimates for solutions to the Cauchy problem of the Debye-Huckel system, Nonlinear Differ. Equ. Appl. , 19 (2012), 1–18. (with Dr. Qiao Liu and Prof. Shangbin Cui)

　　29.Weak-strong uniqueness of hydrodynamic flow of nematic liquid crystals, Electron. J. Diff. Equa. , Vol. 2012, 182 (2012), 1–16. (with Dr. Qiao Liu) 

　　30.Logarithmically improved BKM’s criterion for the 3D nematic liquid crystal flows, Nonlinear Anal. TMA , 75 (2012), 4942–4949. (with Dr. Qiao Liu and Prof. Shangbin Cui)

　　31.A logarithmically improved regularity criterion for the Navier-Stokes equations, Monatsh Math. , 167 (2012), 503–509. (with Dr. Qiao Liu and Prof. Shangbin Cui)

　　32.Existence and regularizing rate estimates of solutions to a generalized MHD system in pseudo measure spaces, Annali di Matematica , 191 (2012), 293–309. (with Dr. Qiao Liu and Prof. Shangbin Cui)

　　33.Well-posedness of a dissipative system modeling electrohydrodynamics in Lebesgue spaces, Diff. Equa. Appl. , 3(3) (2011), 427–448. (with Dr. Chao Deng and Prof. Shangbin Cui)

　　34.Remarks on the local existence of solutions to the Debye system, J. Math. Anal. Appl. , 383 (2011), 337–343. (with Prof. Shangbin Cui)

　　35.Well-posedness for the NSNPP system in Triebel-Lizorkin space and Besov space with negative indices, J. Math. Anal. Appl. , 377 (2011), 392–405. (with Dr. Chao Deng and Prof. Shangbin Cui)

　　36.A regularity criterion for the three-dimensional nematic liquid crystal flow in terms of one directional derivative of the velocity, J. Math. Phys. , 52 (2011), 033102. (with Dr. Qiao Liu and Prof. Shangbin Cui)

　　37.Global well-posedness of a dissipative system arising in electrohydrodynamics in negative-order Besov spaces, J. Math. Phys. , 51, 093101(2010). (with Dr. Chao Deng and Prof. Shangbin Cui)

　　38.A parabolic-hyperbolic free boundary problem modeling tumor growth with drug application, Electron. J. Diff. Equa. , Vol. 03 (2010), 1–18.

　　39.Well-posedness of a dissipative nonlinear electrohydrodynamic system in modulation spaces, Nonlinear Anal. TMA. , 73 (2010), 2088–2100. (with Dr. Chao Deng and Prof. Shangbin Cui)

　　40.Existence of infinitely many weak solutions for the p -Laplacian with nonlinear boundary conditions, Nonlinear Anal. TMA. , 69 (2008), 1343–1355. (with Prof. Peihao Zhao)

　　41.Infinitely many weak solutions for a p -Laplacian equation with nonlinear boundary conditions, Electron. J. Diff. Equa. , Vol. 90 (2007), 1–14. (with Prof. Peihao Zhao)

　　六、学术会议及访问

　　2015年7月—9月  北京应用物理与计算数学研究所 访问江松院士

　　2015年5月22—25日 华中师范大学 调和分析及其应用国际会议(The International Conference on Harmonic Analysis and Application)

　　2014年8月20—22日 兰州大学 非线性分析与动力系统学术研讨会(Workshop on Nonlinear Analysis and Dynamical Systems)

　　2013年7月—9月  浙江大学数学系 访问张挺教授

　　2012年7月1—3日 华南师范大学 液晶流的数学分析及应用(Workshop on Mathematical Analysis and Applications of Liquid Crystals and Related Topics )

　　2011年7月14—30日 中山大学 第九届非线性偏微分方程暑期讲习班暨学术会议

　　2011年7月11—14日 陕西师范大学 第八届华东偏微分方程会议暨第二届反应扩散方程与生物数学国际研讨会(The 8th East China Partial Differential Equations Conference & The 2nd International Workshop on Reaction-Diffusion Models and Mathematical Biology)

　　七、联系方式

　　通讯地址：陕西省杨凌示范区西农路22号 西北农林科技大学理学院

　　办公室: 理科楼E525

　　邮编：712100

　　邮箱：zhaojih@nwsuaf.edu.cn