Regularity of Holder continuous solutions of the supercritical porous media equation

被引：0
作者：
Yu, Wenxin [1 ]
He, Yigang [2 ]
Tong, Yaonan [1 ]
Luo, Qiwu [1 ]
Wu, Xianming [1 ]
机构：
[1] Hunan Univ, Coll Elect & Informat Engn, Changsha 410082, Hunan, Peoples R China
[2] Hefei Univ Technol, Sch Elect & Automat Engn, Hefei 230009, Anhui, Peoples R China
来源：
BOUNDARY VALUE PROBLEMS | 2013年
关键词：
porous media equation; supercritical dissipation; regularity; weak solutions; QUASI-GEOSTROPHIC EQUATION;
D O I：
10.1186/1687-2770-2013-225
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present a regularity result for weak solutions of the N-dimensional (N = 2 or 3) porous media equation with supercritical (alpha < 1) dissipation Lambda(alpha). If a Leray-Hopf weak solution is Holder continuous theta is an element of C-delta(R-N) with delta > 1 - alpha on the time interval [0, t], then it is actually a classical solution on [0, t].
引用
收藏
页数：10
相关论文
共 50 条
  • [1] Regularity of Hölder continuous solutions of the supercritical porous media equation
    Wenxin Yu
    Yigang He
    Yaonan Tong
    Qiwu Luo
    Xianming Wu
    Boundary Value Problems, 2013
  • [2] Regularity of Holder continuous solutions of the supercritical quasi-geostrophic equation
    Constantin, Peter
    Wu, Jiahong
    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2008, 25 (06): : 1103 - 1110
  • [3] Holder Regularity for the Linearized Porous Medium Equation in Bounded Domains
    Jin, Tianling
    Xiong, Jingang
    ANALYSIS IN THEORY AND APPLICATIONS, 2024, 40 (02): : 111 - 171
  • [4] Holder continuity of solutions of supercritical dissipative hydrodynamic transport equations
    Constantin, Peter
    Wu, Jiahong
    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2009, 26 (01): : 159 - 180
  • [5] Higher Regularity of Holder Continuous Solutions of Parabolic Equations with Singular Drift Velocities
    Friedlander, Susan
    Vicol, Vlad
    JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2012, 14 (02) : 255 - 266
  • [6] On the regularity at shrinking points for the porous media equation
    Jacqueline Mossino
    Maura Ughi
    Nonlinear Differential Equations and Applications NoDEA, 2000, 7 : 1 - 21
  • [7] EVENTUAL REGULARITY OF THE SOLUTIONS TO THE SUPERCRITICAL DISSIPATIVE QUASI-GEOSTROPHIC EQUATION
    Dabkowski, Michael
    GEOMETRIC AND FUNCTIONAL ANALYSIS, 2011, 21 (01) : 1 - 13
  • [8] Eventual Regularity of the Solutions to the Supercritical Dissipative Quasi-Geostrophic Equation
    Michael Dabkowski
    Geometric and Functional Analysis, 2011, 21 : 1 - 13
  • [9] Holder continuous solutions of Boussinesq equation with compact support
    Tao, Tao
    Zhang, Liqun
    JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 272 (10) : 4334 - 4402
  • [10] Regularity of weak solutions and supersolutions to the porous medium equation
    Boegelein, Verena
    Lehtelae, Pekka
    Sturm, Stefan
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 185 : 49 - 67
12345