基本信息
曹道民  男  博导  中国科学院数学与系统科学研究院
电子邮件: dmcao@amt.ac.cn
通信地址: 北京市海淀区中关村东路55号
邮政编码: 100190

研究领域

非线性偏微分方程, 非线性分析

招生信息

   
招生专业
070104-应用数学
招生方向
偏微分方程
非线性分析

教育背景

1986-09--1989-06   中国科学院系统科学研究所   理学博士
1983-07--1986-07   湖南省湘潭大学数学系   理学硕士
1979-09--1983-07   湖南省湘潭大学数学系   理学学士
学历
-- 研究生
学位
-- 博士

工作经历

1997-10~2020-04,中国科学院数学与系统科学研究院, 研究员
1993-11~1997-09,中国科学院武汉数学物理研究所, 研究员
1991-01~1993-10,中国科学院武汉数学物理研究所, 副研究员
1989-06~1990-12,中国科学院武汉数学物理研究所, 助理研究员


教授课程

微积分III-B
微积分Ⅱ-B
微积分I-B

专利与奖励

   
奖励信息
(1) 湖北省自然科学奖, 二等奖, 省级, 2000
(2) 中国科学院青年科学家奖, 一等奖, 院级, 1999
(3) 中国科学院自然科学奖, 二等奖, 部委级, 1991

科研活动


1. 国家自然科学基金面上项目,11771469,非局部薛定谔方程解的长时间行为的变分法的研究,2018/01-2021/12在研参与。

2. 国家自然科学基金重点项目,11331010,现代变分问题的若干问题研究,2014/01-2018/12,参与。

3. 国家自然科学基金面上项目,11271354,带间断非线性项椭圆型偏微分方程,2013/01-2016/12,已结题,主持

4. 国家自然科学基金重点项目,10631030,非线性椭圆与抛物型方程的理论及其应用研究,2007/01-2010/12,已结题,参加

5. 中国科学院知识创新工程重要方向性项目《数学物理中的若干重大问题》,2007/01-2009/12,已结题,主持

6. 973 项目“数学与其它领域交叉的若干专题”子课题《流体力学与材料科学中的偏微分方程》,2006/01-2010/12,参加,骨干成员

7. 国家自然科学基金杰出青年基金项目,10425104,非线性偏微分方程,2005/01-2008/12,已结题,主持

8. 973项目“核心数学的若干前沿问题”子项目《非线性偏微分方程》, G1990751,1999/01-2004/12,已结题,参加

9.  国家自然科学基金项目面上项目,19871091,非线性椭圆型方程的多峰解,1998/01-2001/12,已结题,主持

10. 中国科学院 “ **** ”, 1997/01-1999/12,已结题,主持。



在研项目
( 1 ) 非光滑变分理论及其在椭圆型偏微分方程中的应用, 参与, 国家级, 2019-01--2023-12
( 2 ) 前沿科学重点研究相目-带间断的非线性偏微分方程, 主持, 部委级, 2017-01--2021-12
近年发表论文


[1] Daomin Cao, Multiscale steady vortex patches for 2D incompressible Euler equations, SIAM Journal on Mathematical Analysis, 54(2022), 1488-1514.(with Jie Wan)

[2] Daomin Cao, On the global classical solutions for the generalized SQG equation, Journal of Functional Analysis, 283 (2022) art.109503.(with Guolin Qin,Weicheng Zhan and Changjun Zou)

[3] Daomin Cao, Traveling vortex pairs for 2D incompressible Euler equations Calculus of Variations and Partial Differential Equations, 2021, 60:190with Shanfa Lai and Weicheng Zhan

[4] Daomin Cao, Singularly Perturbed Methods for Nonlinear Elliptic Problems, Cambridge University Press, 2021, ISBN 9781108836838.with Shuangjie Peng and Shusen Yan

[5] Daomin Cao, The number of positive solutions to the Brezis-Nirenberg problem, Trans. Amer. Math. Soc., 374 (2021), 1947 - 1985.( with P. Luo and S. Peng)

[6] Daomin cao, Super poly-harmonic properties, Louville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians, Trans. Amer. Math. Soc., 374 (2021), 4781-4813. (with Wei Dai and Guolin Qin)

[7] Daomin Cao, Steady vortex patches near a nontrivial irrotational flow, Science China Mathematics, 64(2021), 947-962. (with Guodong Wang and Weicheng Zhan)

[8] Daomin Cao, Desingularization of vortices for 2D steady Euler flows via the vorticity method, SIAM J. Math.Anal. ,522020)5363-5388 with G. Wang and W. Zhan

[9] Daomin Cao, Existence of Steady Multiple Vortex Patches to the Vortex-wave System, Pacific Math. J.,308(2020), 257-279. (with Guodong Wang

[10] Daomin Cao, Steady vortex patches with opposite rotation directions in a planar ideal fluidCalculus of Variations and Partial Differential Equations, 58(2019) 58:75 with Guodong Wang

[11] Daomin Cao, Steady vortex patch solutions to the vortex-wave systemNonlinearity32(2019),1182-1904with Guodong Wang

[12] Daomin Cao, Nonlinear orbital stability for planar vortex patches, Proceedings of the American Mathematical Society,147(2019),775-784.(with Jie Wan and Guodong Wang)

[13] Daomin Cao, Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity, Proceedings of the Royal Society of Edinburgh, 149(2019),979-994. (with Wei Dai)

[14] Daomin Cao, Local uniqueness for vortex patch problem in incompressible planar steady flow, Journal de Mathematiques Pures et Appliquees, 131 ( 2019 ), 251-289.(with Yuxia Guo, Shuangjie Peng and Shusen Yan)

[15] Daomin Cao, Sign-changing bubble tower solutions for the supercritical Hénon-type equations, Ann. Mat. Pura. Appl. ,197(2018),1227–1246.(with Zhongyuan Liu and Shuangjie Peng)

[16] Daomin Cao, Nodal solutions for a supercritical semilinear problem with variable exponent,Calculus of Variations and Partial Differential Equations, 57(2018), Art. 38, 19 pp. (with Zhongyuan Liu and Shuanglong Li)

[17] Cao Daomin, Non-stationary Navier-Stokes equations with mixed boundary conditions, J. Math. Sci. Univ. Tokyo, 24 (2017), no. 2, 159–194. (with Kim Tujin)

[18] Cao Daomin, The steady Navier-Stokes and Stokes systems with mixed boundary conditions including one-sided leaks and pressure, Methods Appl. Anal., 23 (2016), no. 4, 329–363. (with Kim Tujin)

[19] Cao Daomin, Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations, Calc. Var. Partial Differential Equations, 54 (2015), 4037– 4063.(with Li Shuanglong and Luo Peng)

[20] Cao Daomin, Dynamics for a stochastic reaction-diffusion equation with additive noise, J. Differential Equations, 259 (2015), 838–872.(with Sun Chunyou and Yang Meihua)

[21] Cao Daomin, Planar vortex patch problem in incompressible steady flow. Adv. Math., 270 (2015), 263–301. (with Peng Shuangjie and Yan Shusen)

[22]. Daomin Cao, Regularization of point vortices for the Euler equation in dimension two, Arch. Rat. Mech. Anal., 212(2014),179-217.(with Zhongyuan Liu and Juncheng Wei)
[23]. Daomin Cao, Minimal blow-up solutions of mass-critical inhomogeneous Hartree equation. J. Math. Phys. 54 (2013), no. 12, 121511, 25 pp. (with Su Yiming)
[24]. Daomin Cao, On the Webster scalar curvature problem on the CR sphere with a cylindrical-type symmetry. J. Geom. Anal. 23 (2013), no. 4, 1674-1702.( Peng Shuangjie and Yan Shusen)
[25]. Daomin Cao, Continuous dependence of Cauchy problem for nonlinear Schrödinger equation in H^s. J. Differential Equations, 255 (2013), no. 7, 2018--2064. (with Dai Wei and Yang Weihua)
[26]. Daomin Cao, Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth, J. Functional Analysis, 262(2012), 2861-2902 (with S.Peng and S.Yan)
[27]. Daomin Cao
Infinitely many solutions for an elliptic Neumann problem involving critical Sobolev growth, J. Differential Equations, 251(2011), 1389 -1414, (with S.Yan)
[28]. Daomin Cao
Convergence of solutions to the 5D Hartree equations, Colloquium Mathematicum, 125(2011), 427-445, (with Qing Guo)
[29]. Daomin Cao
On ground states of spinor Bose-Einstein condensates, Nonlinear Differential Equation and Application, 18(2011), 427-445, (with J.Wei and I.L.Chern)
[30]. Daomin Cao, Multiplicity of solutions for the plasma problem in two dimension, Advances in Mathematics, 225(2010),  2741-2785.
with S.Peng and S.Yan
[31]. Daomin Cao, Local exact controlability of the Navier-Stokes equations with condition on the pressure on part of the boundary, SIAM J. Control and Optim., 45(2010), 3805 -3837. (with T.J. Kim)
[32]. Daomin Cao, Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential, Calculus of Variations and PDE., 38(2010), 471-501. (with Shusen Yan)
[33] Cao, Daomin, Inhomogeneous critical nonlinear Schrouml;dinger equations with a harmonic potential, J. Math. Phys. , 51(2010)
no. 4, 043505, 24 pp. (with Han Pigong)

 

 




学术兼职

《应用数学学报》副主编,《数学物理学报》副主编, 《Applicable Analysis》《Annales Academiae Scientiarum Fennicae, Mathematica》等刊物的编委。

指导学生

已指导学生

杨卫华  博士研究生  070104-应用数学  

韩丕功  博士研究生  070104-应用数学  

彭双阶  博士研究生  070104-应用数学  

唐仲伟  博士研究生  070104-应用数学  

温海瑞  博士研究生  070104-应用数学  

王云鹏  硕士研究生  070104-应用数学  

赵雷嘎  博士研究生  070104-应用数学  

袁建军  博士研究生  070104-应用数学  

张振辉  博士研究生  070104-应用数学  

高善国  博士研究生  070104-应用数学  

郭青  博士研究生  070104-应用数学  

戴蔚  博士研究生  070104-应用数学  

刘忠原  博士研究生  070104-应用数学  

吴丹  博士研究生  070104-应用数学  

苏一鸣  博士研究生  070104-应用数学  

张杨  博士研究生  070104-应用数学  

孙丕业  博士研究生  070104-应用数学  

李双龙  博士研究生  070104-应用数学  

李航  博士研究生  070104-应用数学  

王国栋  博士研究生  070104-应用数学  

现指导学生

万捷  博士研究生  070104-应用数学  

秦国林  博士研究生  070104-应用数学  

詹伟城  博士研究生  070104-应用数学  

赖善发  博士研究生  070104-应用数学  

余伟林  博士研究生  070104-应用数学  

邹昌君  博士研究生  070104-应用数学