GLOBAL EXISTENCE OF WEAK EVEN SOLUTIONS FOR AN ISOTROPIC LANDAU EQUATION WITH COULOMB POTENTIAL

被引：9

作者：

Gualdani, Maria Pia ^{[1
]}

Zamponi, Nicola ^{[2
]}

机构：

[1] George Washington Univ, Dept Math, Washington, DC 20052 USA

[2] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2018年 / 50卷 / 04期

基金：

奥地利科学基金会;

关键词：

Landau equation; isotropic diffusion; weak solutions; regularization; SOBOLEV INEQUALITIES; FRACTIONAL INTEGRALS; OPERATORS;

D O I：

10.1137/17M1142685

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider an isotropic modification for the Landau equation with Coulomb potential in three space dimensions. Global in time existence of weak solutions for even initial data is shown by employing a time semidiscretization of the equation, an entropy inequality, and a uniform estimate for the second moment of the solution to the discretized problem. Moreover, under an additional condition that has to be satisfied uniformly over time, uniform boundedness of the solution is proved, with bounds depending solely on the mass, second moment, and entropy of the solution. A byproduct of our analysis is a proof of improved regularity for weak solutions to the Landau equation with Coulomb potential.

引用

页码：3676 / 3714

页数：39

共 15 条

[11] The boundedness-by-entropy method for cross-diffusion systems [J].

Juengel, Ansgar .

NONLINEARITY, 2015, 28 (06) :1963-2001

[12]

Jungel A., 2016, Entropy methods for diffusive partial differential equations

[13] Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity [J].

Krieger, Joachim ;

Strain, Robert M. .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2012, 37 (04) :647-689

[14] WEIGHTED INEQUALITIES FOR FRACTIONAL INTEGRALS ON EUCLIDEAN AND HOMOGENEOUS SPACES [J].

SAWYER, E ;

WHEEDEN, RL .

AMERICAN JOURNAL OF MATHEMATICS, 1992, 114 (04) :813-874

[15] On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations [J].

Villani, C .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1998, 143 (03) :273-307

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