\( \def\<#1>{\left<#1\right>} \newcommand{\CC}{\mathcal{C}} \newcommand{\eps}{\varepsilon} \newcommand{\ls}{\leqslant} \newcommand{\gs}{\geqslant} \newcommand{\norm}[1]{\|#1\|} \usepackage{resmes} \newcommand{\mres}{\resmes} \usepackage{cases} \newcommand{\dv}{\mathrm{div}} \newcommand{\R}{\mathbb{R}} \newcommand{\D}{\partial} \)
郝成春 科研论著
ResearchGate, arXiv, MathSciNet, Google Scholar, ORCID
合作者[合作次数]Li Hai-Liang (李海梁)10, Yang Siqi (杨思奇)9, Hsiao Ling (肖玲)8, Zhang Wei (张伟)8, Luo Tao (罗涛)6, Fu Jie (付杰)5, Wang Baoxiang (王保祥)4, Guo Zihua (郭紫华)1, Hudzik Henryk1, Huo Zhaohui(霍朝辉) 1, Jia Yueling (贾月玲)1, Lin Yiquan (林义筌)1, Wang Dehua (王德华)1, Zhang Guo-Jing (张国敬)1, Zhang Min (张敏)1.

预印本

  1. Fu, Jie and Hao, Chengchun and Zhang, Wei;
    On the splash singularity for the free-boundary problem of incompressible elastodynamics
    In preparation, 2025.
  2. Hao, Chengchun and Luo, Tao and Yang, Siqi;
    A blow-up criterion for the incompressible Euler equations with surface tension and a closed free surface
    In preparation, 2025.
  3. Hao, Chengchun and Luo, Tao and Yang, Siqi;
    Exponential stability of a free boundary problem with spherical symmetry for a gas bubble immersed in a bounded incompressible liquid
    Submitted, 2024.
  4. Zhang, Wei and Fu, Jie and Hao, Chengchun and Yang, Siqi;
    Global well-posedness of the free boundary problem for incompressible viscous resistive MHD in critical Besov spaces
    Submitted, 2024.
  5. Hao, Chengchun and Yang, Siqi;
    A prior estimates and a blow-up criterion for the incompressible ideal MHD equations with surface tension and a closed free surface
    Submitted, 2023.

拟出版讲义

Introduction to Harmonic Analysis (调和分析导论, 英文版), 拟出版, 2024. [目录]

    已出版著作

    Wang, Baoxiang and Huo, Zhaohui and Hao, Chengchun and Guo, Zihua;
    Harmonic Analysis Method for Nonlinear Evolution Equations,I
    World Scientific Pub Co Inc 300pp, 2011.   
    [中文版: 非线性发展方程的调和分析方法(I)适定性理论 (未出版, 2010) 下载]

    已接受/发表论文

    ■ 流体方程的自由边界问题

    ♣ 磁流体方程
  1. Hao, Chengchun and Yang, Siqi;
    On a regularity criterion for free boundary incompressible ideal MHD with surface tension
    To appear, Communications in Information and Systems, 25: 18pp, 2025.
  2. Hao, Chengchun and Yang, Siqi;
    Splash singularity for the free boundary incompressible viscous MHD
    Journal of Differential Equations, 379: 26–103, 2024.
  3. Fu, Jie and Hao, Chengchun and Yang, Siqi and Zhang, Wei;
    A Beale-Kato-Majda criterion for free boundary incompressible ideal magnetohydrodynamics
    Journal of Mathematical Physics, 64(9): No.091505, 16pp, 2023.
  4. Hao, Chengchun and Zhang, Wei;
    A priori estimates for free boundary problem of 3D incompressible inviscid rotating Boussinesq equations
    Zeitschrift für angewandte Mathematik und Physik, 74(2): No.80, 21pp, 2023.
  5. Hao, Chengchun and Luo, Tao;
    Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations
    Electronic Research Archive, 30(2): 404-424, 2022.
  6. Hao, Chengchun and Luo, Tao;
    Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations
    Journal of Differential Equations, 299: 542-601, 2021.
  7. Hao, Chengchun and Luo, Tao;
    Ill-posedness of free boundary problem of the incompressible ideal MHD
    Communications in Mathematical Physics, 376(1): 259–286, 2020.
  8. Hao, Chengchun;
    On the motion of free interface in ideal incompressible MHD
    Archive for Rational Mechanics and Analysis, 224(2): 515–553, 2017.
  9. Hao, Chengchun and Luo, Tao;
    A priori estimates for free boundary problem of incompressible inviscid magnetohydrodynamic flows
    Archive for Rational Mechanics and Analysis, 212(3): 805-847, 2014.

  10. ♣ 两相流方程
  11. Zhang, Wei and Fu, Jie and Hao, Chengchun and Yang, Siqi;
    Global well-posedness for two-phase fluid motion in the Oberbeck-Boussinesq approximation
    Journal of Mathematical Physics, 65(8): No.081509, 22pp, 2024.
  12. Hao, Chengchun and Zhang, Wei;
    Local well-posedness for two-phase fluid motion in the Oberbeck-Boussinesq approximation
    Communications on Pure and Applied Analysis, 22(7): 2099-2131, 2023.
  13. Hao, Chengchun and Zhang, Wei;
    Maximal $ L^p$-$ L^q$ regularity for two-phase fluid motion in the linearized Oberbeck-Boussinesq approximation
    Journal of Differential Equations, 322: 101-134, 2022.

  14. ♣ 弹性方程
  15. 付杰, 郝成春, 杨思奇, 张伟;
    不可压新Hooke 型弹性动力学自由边界问题的爆破准则
    中国科学:数学55(3): 635∼650, 2025.
  16. Hao, Chengchun and Wang, Dehua;
    A priori estimates for the free boundary problem of incompressible neo-Hookean elastodynamics
    Journal of Differential Equations261(1): 712–737, 2016.    

  17. ♣ Euler方程
  18. Hao, Chengchun;
    Remarks on the free boundary problem of compressible Euler equations in physical vacuum with general initial densities
    Discrete and Continuous Dynamical Systems - B, 20(9): 2885-2931, 2015.

  19. ■ 流体方程Cauchy问题的适定性

  20. Hao, Chengchun and Li, Hai-Liang;
    Well-posedness for a multidimensional viscous liquid-gas two-phase flow model
    SIAM J. Math. Anal., 44(3): 1304–1332, 2012.
  21. Hao, Chengchun;
    Global well-posedness for a multidimensional chemotaxis model in critical Besov spaces
    Zeitschrift für angewandte Mathematik und Physik, 63(5): 825-834, 2012.
  22. Lin, Yiquan and Hao, Chengchun and Li, Hai-Liang;
    Global well-posedness of compressible bipolar Navier-Stokes-Poisson equations
    Acta Mathematica Sinica, English Series, 28(5): 925-940, 2012.
  23. Hao, Chengchun;
    Well-posedness for the viscous rotating shallow water equations with friction terms
    J. Math. Phys., 52(2): No.023101, 12pp, 2011.
  24. Hao, Chengchun;
    Well-posedness to the compressible viscous magnetohydrodynamic system
    Nonlinear Analysis: Real World Applications, 12(6): 2962–2972, 2011.
  25. Hao, Chengchun;
    Cauchy problem for viscous shallow water equations with surface tension
    Discrete Contin. Dyn. Syst. Ser. B, 13(3): 593-608, 2010.
    We are concerned with the Cauchy problem for a viscous shallow water system with a third-order surface-tension term. The global existence and uniqueness of the solution in the space of Besov type is shown for the initial data close to a constant equilibrium state away from the vacuum by using the Friedrich's regularization and compactness arguments.
  26. Hao, Chengchun and Hsiao, Ling and Li, Hai-Liang;
    Cauchy problem for viscous rotating shallow water equations
    Journal of Differential Equations, 247(12): 3234–3257, 2009.
  27. Hao, Chengchun and Li, Hai-Liang;
    Global existence for compressible Navier–Stokes–Poisson equations in three and higher dimensions
    Journal of Differential Equations, 246(12): 4791–4812, 2009.

  28. ■ 弥散型方程初(边)值问题的适定性

  29. 郝成春;
    几类弥散型非线性偏微分方程组的研究进展
    2007中国科学院优博论丛,  科学出版社, 北京, 1--6, 2008.
  30. Hao, Chengchun and Hsiao, Ling and Li, Hai-Liang;
    Global well posedness for the Gross–Pitaevskii equation with an angular momentum rotational term
    Math. Methods Appl. Sci., 31(6): 655-664, 2008.
  31. Hao, Chengchun and Hsiao, Ling and Li, Hai-Liang;
    Global well posedness for the Gross-Pitaevskii equation with an angular momentum rotational term in three dimensions
    J. Math. Phys., 48(10): No.102105, 11pp, 2007.
  32. Hao, Chengchun;
    Well-posedness for one-dimensional derivative nonlinear Schr\"odinger equations
    Commun. Pure Appl. Anal., 6(4): 997-1021, 2007.
  33. Hao, Chengchun and Hsiao, Ling and Wang, Baoxiang;
    Well-posedness of Cauchy problem for the fourth order nonlinear Schr\"odinger equations in multi-dimensional spaces
    Journal of Mathematical Analysis and Applications, 328(1): 58-83, 2007.
  34. Hao, Chengchun and Hsiao, Ling and Wang, Baoxiang;
    Wellposedness for the fourth order nonlinear Schr\"odinger equations
    Journal of Mathematical Analysis and Applications, 320(1): 246-265, 2006.
  35. Wang, Baoxiang and Hao, Chengchun and Hudzik, Henryk;
    Energy scattering theory for the nonlinear Schr\"odinger equations with exponential growth in lower spatial dimensions
    Journal of Differential Equations, 228(1): 311-338, 2006.
  36. Hao, Chengchun;
    The initial boundary value problem for quasi-linear Schr\"odinger-Poisson equations
    Acta Math. Sci. Ser. B Engl. Ed., 26(1): 115-124, 2006.
  37. Hao, Chengchun and Hsiao, Ling;
    Studies on Schr\"odinger-Poisson systems (Excerpt of Dissertation)
    J. Grad. Sch. of CAS, 22(5): 141-146, 2005.
  38. Hao, Chengchun and Li, Hai-Liang;
    On the initial value problem for the bipolar Schr\"odinger-Poisson systems
    J. Partial Diff. Eqns., 17(3): 283-288, 2004.
  39. Hao, Chengchun and Hsiao, Ling and Li, Hai-Liang;
    Modified scattering for bipolar nonlinear Schr\"odinger-Poisson equations
    Math. Models Methods Appl. Sci., 14(10): 1481-1494, 2004.
  40. Hao, Chengchun and Hsiao, Ling;
    Large time behavior and global existence of solution to the bipolar defocusing nonlinear Schr\"odinger-Poisson system
    Quart. Appl. Math., 62(4): 701-710, 2004.
  41. Hao, Chengchun;
    Energy scattering for the generalized Davey-Stewartson equations
    Acta. Math. Appl. Sinica, 19(2): 333-340, 2003.
  42. 郝成春;
    关于非线性Davey-Stewartson方程的散射理论
    数学研究与评论, 23(4), 645-650, 2003.   
  43. Hao, Chengchun;
    Energy scattering for the generalized Davey-Stewartson equations (科技创新快报)
    Hebei Uni., Rat. Sci. Edt., 22(1), 73-74, 2002.

  44. ■ 量子模型初(边)值问题的适定性或渐近行为

  45. Li, Hai-Liang and Zhang, Guo-Jing and Zhang, Min and Hao, Chengchun;
    Long-time self-similar asymptotic of the macroscopic quantum models
    J. Math. Phys., 49(7): No.073503, 14pp, 2008.
  46. Hao, Chengchun and Jia, Yueling and Li, Hai-Liang;
    Quantum Euler-Poisson system: local existence of solutions
    J. Partial Diff. Eqns., 16(4): 306-320, 2003.

学位论文

  • 博士学位论文: 几类弥散型非线性偏微分方程组的研究, 2005.
  • 硕士学位论文: Energy Scattering for the Generalized Davey-Stewartson Equations (英文), 2002.