更新日期：2018年9月9日
姓 名 李用声 性 别 男
出生年月 1965年7月 籍贯 湖北南漳县
民 族 汉族 政治面貌 无党派
最后学历 博士研究生 最后学位 理学博士
技术职称 教授 导师类别 博、硕导
行政职务 副所长 Email yshli@scut.edu.cn
工作单位 数学学院、数学研究所 邮政编码 510640
通讯地址 华南理工大学4号楼
单位电话 **


个人简介
李用声 男，1965年7月生于湖北省襄阳市。华南理工大学数学系教授、博士生导师。
工作经历
1988年7月—1995年12月 在华中理工大学数学系任教；历任助教、讲师。

1995年12月—1998年6月 在北京应用物理与计算数学研究所博士后流动站做博士后。

1998年7月—2002年9月 在华中理工大学数学系任教，历任副教授、教授。

2002年10月—现在 华南理工大学数学学院任教。二级教授。
教育经历
1981年9月—1985年7月 在华东师范大学数学系读大学，获得学士学位。

1985年9月—1988年6月 在华东师范大学数学系读研究生，获得硕士学位。

1991年9月—1995年12月 在华中理工大学数学系读博士研究生，1996年6月获得博士学位。
获奖、荣誉称号
1998年无穷维动力系统的理论研究及其应用，国防科工委科技进步一等奖(第三完成人) 。

1998年被评为湖北省跨世纪学术骨干。

2012年全国优秀博士学位论文提名论文指导老师。
社会、学会及学术兼职
广东省数学会副秘书长、常务理事。
研究领域
主要研究方向：非线性发展方程
科研项目
1995年——1997年 主持一项湖北省自然科学基金项目（非线性发展方程与无穷维动力系统）。

2001年——2003年 主持一项国家自然科学基金项目(数学物理中某些非线性发展方程的适定性和长时间性态)。

2005年——2007年 主持一项国家自然科学基金项目(数学物理中某些非线性偏微分方程)。

2008年——2010年 主持一项国家自然科学基金项目(数学物理中非线性Schrodinger型方程的研究)。

2012年——2015年 主持一项国家自然科学基金项目(Davey-Stewartson 型方程组的适定性和爆破性研究）。

2013——2014年 主持广东省优秀博士论文作者资助项目（两类非线性发展方程的适定性研究）。

2016年——2019年 主持一项国家自然科学基金项目(拟线性Schrodinger型方程的适定性和爆破性）。
发表论文
主要从事非线性偏微分方程和无穷维动力系统的研究。涉及的方程有Schrodinger型方程和方程组、流体力学方程组、Ginzburg-Landau方程、KdV型和Camassa-Holm型方程。研究的内容包括这些方程（组）解的存在性、唯一性、爆破性、衰减性、整体吸引子的存在性、整体吸引子的分形维数估计等问题。在国内外重要学术刊物、论文集上发表论文90 余篇，SCIE收录69篇。指导的博士生曾获得全国百篇优秀博士论文提名奖。

1.Yan Wei; Li Yongsheng; Huang Jianhua; Duan Jinqiao. The Cauchy problem for the Ostrovsky equation with positive dispersion. NODEA-Nonlinear Differential Equations and Applications, Vol 25, No. 3, 2018, 25:22. DOI: 10.1007/s00030-018-0514-x.

2.Zhai Xiaoping; Li Yongsheng; Yan Wei. Global well-posedness for the 3D viscous nonhomogeneous incompressible magnetohydrodynamic equations. Analysis and Applications, Vol. 16, No. 3, 2018, 363-405. DOI: 10.1142/S**0014.

3.Zhao Yongye; Yang Meiling; Li Yongsheng. Non-uniform dependence for the periodic higher dimensional Camassa-Holm equations. Journal of Mathematical Analysis and Applications, Vol. 461, No. 1, 2018, 59-73. DOI: 10.1016/j.jmaa.2018.01.012.

4.Ren Yuanyuan; Li Yongsheng; Yan Wei. Sharp well-posedness of the cauchy problem for the fourth order nonlinear schrodinger equation. Communications on Pure and Applied Analysis, Vol. 17, No. 2, 2018, 487-504. DOI: 10.3934/cpaa.**.

5.Xu Huan; Li Yongsheng; Chen Fei. Global Solution to the Incompressible Inhomogeneous Navier-Stokes Equations with Some Large Initial Data. Journal of Mathematical Fluid Mechanics, Vol. 19, No. 2, 2017, 315-328. DOI: 10.1007/s00021-016-0282-5.

6.Zhai Xiaoping; Li Yongsheng; Yan Wei. Global solution to the 3-D density-dependent incompressible flow of liquid crystals. Nonlinear Analysis-Theory Methods & Applications Vol. 156, 2017, 249-274. DOI: 10.1016/j.na.2017.02.020.

7.Yan Wei; Li Yongsheng; Zhai Xiaoping; Zhang Yimin. The Cauchy Problem for the Shallow Water Type Equations in Low Regularity Spaces on the Circle. Advances in Differential Equations, Vol.22, Nos.5-6, 2017, 363-402.

8.Chen Fei; Li Yongsheng; ZhaoYongye. Global well-posedness for the incompressible MHD equations with variable viscosity and conductivity. Journal of Mathematical Analysis and Applications, Vol. 447, No. 2, 2017, 1051-1071. DOI: 10.1016/j.jmaa.2016.10.059.

9.Ma Haitao; Zhai Xiaoping; Yan Wei; Li Yongsheng. Global strong solution to the 3D incompressible magnetohydrodynamic system in the scaling invariant Besov-Sobolev-type spaces. Zeitschrift fur Angewandte Mathematik und Physik, Vol. 68, No. 1, 2017, 68:14. DOI: 10.1007/s00033-016-0761-9.

10.Zhai Xiaoping; Li Yongsheng; Xu Huan. Global well-posedness for the 2-D nonhomogeneous incompressible MHD equations with large initial data. Nonlinear Analysis-Real World Applications, Vol. 33, No. 1-18.2017. DOI: 10.1016/j.nonrwa.2016.05.009.

11.Li Shiming; Li Yongsheng; Yan Wei. A Global Existence and Blow-Up Threshold for Davey-Stewartson Equations in R^3. Discrete and Continuous Dynamical Systems-Series S, Vol. 9, No. 6, 2016, 1899-1912. DOI: 10.3934/dcdss.**.

12.Zhai Xiaoping; Li Yongsheng; Yan Wei. Well-Posedness for the Three Dimension Magnetohydrodynamic System in the Anisotropic Besov Spaces. Acta Applicandae Mathematicae, Vol. 143, No. 1, 2016, 1-13. DOI: 10.1007/s10440-015-0024-3.

13.Chen Fei; Li Yongsheng; Xu Huan. Global Solution to the 3D Nonhomogeneous Incompressible MHD Equations with Some Large Initial Data. Discrete and Continuous Dynamical Systems, Vol. 36, No. 6, 2016, 2945-2967. DOI: 10.3934/dcds.2016.36.2945.

14.Xu Huan; Li Yongsheng; Zhai Xiaoping. On the Well-Posedness of 2-D Incompressible Navier-Stokes Equations with Variable Viscosity in Critical Spaces. J. Differential Equations, Vol.260, No. 8, 2016, 6604-6637. DOI: 10.1016/j.jde.2016.01.007.

15.Zhai Xiaoping; Li Yongsheng; Yan Wei. Global Solutions to the Navier-Stokes-Landau-Lifshitz System. Mathematische Nachrichten, Vol. 289, No. 2-3, 2016, 377-388. DOI: 10.1002/mana.**.

16.Zhai Xiaoping; Li Yongsheng; Yan Wei. Global well-posedness for the 3-D incompressible inhomogeneous MHD system in the critical Besov spaces. Journal of Mathematical Analysis and Applications, Vol. 432, No. 1, 2015, 179-195 DOI: 10.1016/j.jmaa.2015.06.048

17.Li Shiming; Yan Wei; Li Yongsheng; Huang Jianhua. The Cauchy Problem for a Higher Order Shallow Water Type Equation on the Circle. J. Differential Equations, Vol. 259, No. 9, 2015, 4863-4896. DOI: 10.1016/j.jde.2015.06.017.

18.Zhai Xiaoping; Li Yongsheng; Yan Wei. Global Well-Posedness for the 3-D Incompressible MHD Equations in the Critical Besov Spaces. Communications on Pure and Applied Analysis, Vol. 14, No. 5, 2015, 1865-1884. DOI: 10.3934/cpaa.2015.14.1865

19.Li Yongsheng; Huang Jianhua; Yan Wei. The Cauchy Problem for the Ostrovsky Equation with Negative Dispersion at the Critical Regularity. J. Differential Equations, Vol. 259, No. 4, 2015, 1379-1408. DOI: 10.1016/j.jde.2015.03.007.

20.Zhao Yongye; Li Yongsheng; Yan Wei. The Global Weak Solutions to the Cauchy problem of the Generalized Novikov Equation. Applicable Analysis, Vol. 94, No. 7, 2015, 1334-1354. DOI: 10.1080/**.2014.930826

21.Zhai Xiaoping; Li Yongsheng. Remarks About the Inviscid Limit for the N-Dimension Magnetohydrodynamic System in the L^p Type Space. Applied Mathematics Letters, Vol. 45, 2015, 37-40. DOI: 10.1016/j.aml.2015.01.009.

22.Chen Defu; Li Yongsheng; Yan Wei. On well-posedness of two-component Camassa-Holm system in the critical Besov space. Nonlinear Analysis-Theory Methods & Applications, Vol. 120, 2015, 285-298. DOI: 10.1016/j.na.2015.03.016

23.Yan Wei; Li Yongsheng. The Cauchy Problem for the Modified Two-Component Camassa-Holm System in Critical Besov Space. Annales de l’Institut Henri Poincare-Analyse Non Lineaire,Vol.32, No. 2, 2015, 443-469. DOI: 10.1016/j.anihpc.2014.01.003.

24.Chen Defu; Li Yongsheng; Yan Wei. On the cauchy problem for a generalized Camassa-Holm equation. Discrete and Continuous Dynamical Systems. Vol. 35, No. 3, 2015, 871-889. DOI: 10.3934/dcds.2015.35.871

25.Yan Wei; Li Yongsheng; Zhang Yimin. The Cauchy problem for the generalized Camassa-Holm equation. Applicable Analysis, Vol. 93, No. 7, 2014, 1358–1381. DOI: 10.1080/**.2013.833325

26.Yan Wei; Li Yongsheng; Zhang Yimin. The Cauchy problem for the generalized Camassa-Holm equation in Besov space. J. Differential Equations 256 (2014), No. 8, 2876–2901. DOI: 10.1016/j.jde.2014.01.023.

27.Zhao Yongye; Li Yongsheng; Yan Wei. Local well-posedness and persistence property for the generalized Novikov equation. Discrete and Continuous Dynamical Systems, Vol. 34, No. 2, 2014, 803-820. DOI: 10.3934/dcds.2014.34.803

28.Yan Wei; Li Yongsheng; Zhang Yimin. The Cauchy problem for the Novikov equation. NoDEA-Nonlinear Differential Equations Appl. Vol. 20, No. 3, 2013, 1157–1169. DOI: 10.1007/s00030-012-0202-1.

29.Yan Wei; Li Yongsheng; Li Shiming. Sharp well-posedness and ill-posedness of a higher-order modified Camassa-Holm equation. Differential Integral Equations, Vol. 25, Nos. 11-12, 2012, 1053–1074.

30.Yan Wei; Li Yongsheng; Zhang Yimin. The Cauchy problem for the integrable Novikov equation. J. Differential Equations, Vol. 253, No. 1, 2012, 298–318. DOI: 10.1016/j.jde.2012.03.015.

31.Yan Wei; Li Yongsheng. Ill-Posedness of Modified Kawahara Equation and Kaup-Kupershmidt Equation. Acta Mathematica Scientia, Vol. 32, No. 2, 2012, 710-716.

32.Yan Wei; Li Yongsheng; Zhang Yimin. Global existence and blow-up phenomena for the weakly dissipative Novikov equation. Nonlinear Anal. Vol. 75, No. 4, 2012, 2464–2473. DOI: 10.1016/j.na.2011.10.044.

33.Yang Xingyu; Li Yongsheng. The global attractor for a weakly damped forced shallow water equation in Sobolev spaces of low regularity. Nonlinear Analysis-Theory Methods & Applications, Vol. 75, No. 4, 2012, 2672-2691. DOI: 10.1016/j.na.2011.11.010.

34.Yan Wei; Li Yongsheng; Yang Xingyu. The Cauchy problem for the modified Kawahara equation in Sobolev spaces with low regularity. Mathematical and Computer Modelling, Vol. 54, No. 5-6, 2011, 1252-1261. DOI: 10.1016/j.mcm.2011.03.036

35.Yan Wei; Li Yongsheng. Ill-posedness of Kawahara equation and Kaup-Kupershmidt equation. J. Math. Anal. Appl. 380, No. 2, 2011, 486–492. DOI: 10.1016/j.jmaa.2011.03.047.

36.Li Yongsheng; Yang Xingyu. Global well-posedness for a fifth-order shallow water equation on the circle. Acta Mathematica Scientia, Vol. 31, No. 4, 2011, 1303-1317.

37.Li Yongsheng; Wu Yifei; Xu Guixiang. Global well-posedness for the mass-critical nonlinear Schr?dinger equation on T. J. Differential Equations 250, No. 6, 2011, 2715–2736. DOI: 10.1016/j.jde.2011.01.025

38.Zhao Caidi; Li Yongsheng; Zhou Shengfan. Random attractor for a two-dimensional incompressible non-Newtonian fluid with multiplicative noise. Acta Mathematica Scientia, Vol. 31, No. 2, 2011, 567-575.

39.Li Yongsheng; Wu Yifei; Xu Guixiang. Low regularity global solutions for the focusing mass-critical NLS in R. SIAM J. Math. Anal. Vol. 43, No. 1, 2011, 322–340. DOI: 10.1137/**.

40.Li Yongsheng; Wu Yifei. Global well-posedness and scattering for the defocusing Hartree equation in R^3. J. Math. Anal. Appl. Vol. 371, No. 1, 2010, 223–232. DOI: 10.1016/j.jmaa.2010.04.054

41.Yan Wei; Li Yongsheng. The Cauchy problem for Kawahara equation in Sobolev spaces with low regularity. Math. Methods Appl. Sci., Vol. 33, No. 14, 2010, 1647–1660. DOI: 10.1002/mma.1273

42.Li Yongsheng; Wu Yifei. Global well-posedness for the Benjamin equation in low regularity. Nonlinear Anal. 73 (2010), No. 6, 1610–1625. DOI: 10.1016/j.na.2010.04.068.

43.Li Yongsheng; Yan Wei; Yang Xingyu. Well-posedness of a higher order modified Camassa-Holm equation in spaces of low regularity. J. Evol. Equ. Vol. 10, No. 2, 2010, 465–486. DOI: 10.1007/s00028-010-0057-z

44.Yang Xingyu; Li Yongsheng. Global well-posedness for a fifth-order shallow water equation in Sobolev spaces. J. Differential Equations, Vol. 248, No. 6, 2010, 1458–1472. DOI: 10.1016/j.jde.2010.01.004.

45.Li Yongsheng; Yang Xingyu. Existence and regularity of the global attractor for a weakly damped forced shallow water equation in H^1(R). Nonlinear Analysis-Theory Methods & Applications, Vol. 71, No. 11, 2009, 5587-5598 DOI: 10.1016/j.na.2009.04.056

46.Zhao Caidi; Li Yongsheng; Zhou Shengfan. Regularity of trajectory attractor and upper semicontinuity of global attractor for a 2D non-Newtonian fluid. J. Differential Equations Vol. 247, No. 8, 2009, 2331–2363. DOI: 10.1016/j.jde.2009.07.031.

47.Zhao Caidi; Zhou Shengfan; Li Yongsheng. Existence and regularity of pullback attractors for an incompressible non-newtonian fluid with delays. Quarterly of Applied Mathematics, Vol. 67, No. 3, 2009, 503-540. DOI: 10.1090/S0033-569X-09-01146-2.

48.Zhao Caidi; Zhou Shengfan; Li Yongsheng. Theorems about the attractor for incompressible non-Newtonian flow driven by external forces that are rapidly oscillating in time but have a smooth average. Journal of Computational and Applied Mathematics, Vol. 220, No. 1-2, 2008, 129-142. DOI: 10.1016/j.cam.2007.08.002.

49.Zhao Caidi; Zhou Shengfan; Li Yongsheng. A note on nonautonomous Klein-Gordon-Schrodinger equations with homogeneous Dirichlet boundary condition. Acta Mathematica Scientia, Vol. 28, No. 4, 2008, 823-833.

50.Zhao Caidi; Zhou Shengfan; Li Yongsheng. Uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid. Applied Mathematics and Computation, Vol. 201, No. 1-2, 2008, 688-700. DOI: 10.1016/j.amc.2008.01.005

51.Zhao, Caidi; Li Yongsheng; Zhou Shengfan. Asymptotic smoothing effect of solutions to Davey-Stewartson systems on the whole plane. Acta Math. Sin. (Engl. Ser.), Vol. 23, 2007, No. 11, 2043–2060. DOI: 10.1007/s10114-007-0949-1.

52.Zhao Caidi; Zhou Shengfan; Li Yongsheng. Trajectory attractor and global attractor for a two-dimensional incompressible non-Newtonian fluid. Journal of Mathematical Analysis and Applications, Vol. 325, No. 2, 2007, 1350-1362. DOI: 10.1016/j.jmaa.2006.02.069

53.Li, Yongsheng. Long Time Behavior for the Weakly Damped Driven Long-Wave--Short-Wave Resonance Equations. J. Differential Equations, Vol. 223, 2006, 261-289. DOI: 10.1016/j.jde.2005.07.006

54.Dong Boqing; Li Yongsheng. Sharp Rate of Decay for Solutions to Non-Newtonian Fluid in R^2. Acta Math. Sinica, Vol. 48, No. 6, 2005, 1065-1070.

55.Zhao Caidi; Li Yongsheng. A note on the asymptotic smoothing effect of solutions to a non-Newtonian system in 2-D unbounded domains. Nonlinear Analysis-Theory Methods & Applications, Vol. 60, No. 3, 2005, 475-483. DOI: 10.1016/j.na.2004.09.014

56.Dong Boqing; Li Yongsheng. Large time behavior to the system of incompressible non-Newtonian fluids in R^2. J. Math. Anal. Appl. Vol. 298, 2004, 667-676. DOI: 10.1016/j.jmaa.2004.05.032.

57.Li Yongsheng; Guo Boling. Attractor of dissipative radially symmetric Zakharov equations outside a ball. Math. Meth. Appl. Sci. Vol. 27, No. 7, 2004, 803–818. DOI: 10.1002/mma.472.

58.Zhao Caidi; Li Yongsheng. H^2-compact attractor for a non-Newtonian system in two-dimensional unbounded domains. Nonlinear Analysis-Theory Methods & Applications, Vol. 56, No. 7, 2004, 1091-1103. DOI: 10.1016/j.na.2003.11.006

59.Li Yongsheng; Guo Boling. Asymptotic smoothing effect of solutions to weakly dissipative Klein–Gordon–Schrodinger equations, J. Math. Anal. Appl., Vol. 282, 2003, 256–265. DOI: 10.1016/S0022-247X(03)00152-5.

60.Li Yongsheng; Guo Boling. Existence and Decay of Weak Solutions to Degenerate Davey-Stewartson Equations. Acta Math. Scientia, Vol. 22. No. 3, 2002, 302-310

61.Li Yongsheng; Guo Boling. Global Attractor for Generalized 2D Ginzburg-Landau Equation. In: “Proceedings of PDE 2000”, Clausthal Germany, July 24-28, 2000, ed M. Demuth, Birkhauser Publishing Hause, 2001, pp 197-204.

62.Li Yongsheng; Guo Boling. Global existence of solutions to the derivative 2D Ginzburg-Landau equation, J. Math. Anal. Appl. Vol. 249, 2000, 412-432.

63.Li Yongsheng; Guo Boling; Jiang Murong. Global existence and blowup of solutions to a degenerate Davey-Stewartson equations. J. Math. Phys., Vol. 41, No. 5, 2000, 2943-2956.

64.Zheng Quan; Li Yongsheng. Abstract parabolic systems and regularized semigroups. Pacific J. of Math., Vol. 182, No. 1, 1998, 183-199.

65.Li Yongsheng; Guo Boling. Attractor for dissipative Zakharov equations in an unbounded domain. Reviews in Math. Phys. Vol. 9, No. 6, 1997, 675-687.

66.Guo Boling; Li Yongsheng. Attractor for dissipative Klein-Gordon-Schrodinger equations in R^3. J. Differential Equations, Vol. 136, No. 2, 1997, 356-377.

67.Li Yongsheng; Chen Qingyi. Long time behavior of ferromagnetic chain equations: Global attractors and their dimension. Math. Methods Appl. Sci. Vol. 20, No. 15, 1997, 1271-1281.

68.Li Yongsheng; Chen Qingyi. Finite dimensional global attractor for dissipative Schrodinger-Boussinesq Equations. J. Math. Anal. Appl. Vol. 205, No.1, 1997, 107-132.

69.Li Yongsheng; Chen Qingyi. On initial boundary value problems for nonlinear Schrodinger equations. Acta Math. Scientia, Vol. 16, No. 4, 1996, 421-431.
教学活动
主讲数学专业的研究生课程：现代分析基础、Sobolev空间、二阶椭圆型方程、非线性发展方程 、非线性泛函分析、线性算子半群及其在PDE中的应用、调和分析等

主讲数学系、工科各院系本科生课程：高等数学、工科数学分析、线性代数、常微分方程、偏微分方程、数学物理方程与特殊函数、复变函数、泛函分析、微分几何等
指导学生情况
毕业博士研究生9名，其中，吴奕飞于2012年获得全国优秀博士学位论文提名论文奖

在读博士研究生5名

毕业硕士研究生29人

在读硕士研究生4人