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

[1]

[Anonymous], 1990, NONLINEAR FUNCTION B

[2] SOME WEIGHTED NORM INEQUALITIES CONCERNING THE SCHRODINGER-OPERATORS [J].

CHANG, SYA ;

WILSON, JM ;

WOLFF, TH .

COMMENTARII MATHEMATICI HELVETICI, 1985, 60 (02) :217-246

[3] LP ESTIMATES FOR FRACTIONAL INTEGRALS AND SOBOLEV INEQUALITIES WITH APPLICATIONS TO SCHRODINGER OPERATIONS [J].

CHANILLO, S ;

WHEEDEN, RL .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1985, 10 (09) :1077-1116

[4] WEIGHTED POINCARE AND SOBOLEV INEQUALITIES AND ESTIMATES FOR WEIGHTED PEANO MAXIMAL FUNCTIONS [J].

CHANILLO, S ;

WHEEDEN, RL .

AMERICAN JOURNAL OF MATHEMATICS, 1985, 107 (05) :1191-1226

[5] Entropy dissipation estimates for the Landau equation in the Coulomb case and applications [J].

Desvillettes, L. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2015, 269 (05) :1359-1403

[6] POSITIVITY OF PSEUDODIFFERENTIAL OPERATORS [J].

FEFFERMAN, C ;

PHONG, DH .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1978, 75 (10) :4673-4674

[7] THE UNCERTAINTY PRINCIPLE [J].

FEFFERMAN, CL .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 9 (02) :129-206

[8] A non-local inequality and global existence [J].

Gressman, Philip T. ;

Krieger, Joachim ;

Strain, Robert M. .

ADVANCES IN MATHEMATICS, 2012, 230 (02) :642-648

[9]

Gualdani M., AP WEIGHTS LANDAU EQ

[10] ESTIMATES FOR RADIAL SOLUTIONS OF THE HOMOGENEOUS LANDAU EQUATION WITH COULOMB POTENTIAL [J].

Gualdani, Maria Pia ;

Guillen, Nestor .

ANALYSIS & PDE, 2016, 9 (08) :1773-1810

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