OPTIMAL TIME DECAY OF THE NON CUT-OFF BOLTZMANN EQUATION IN THE WHOLE SPACE

被引：50

作者：

Strain, Robert M. ^{[1
]}

机构：

[1] Univ Penn, Dept Math, David Rittenhouse Lab, Philadelphia, PA 19104 USA

来源：

关键词：

Kinetic Theory; Boltzmann equation; long-range interaction; non cut-off; soft potentials; hard potentials; fractional derivatives; time decay; convergence rates; GLOBAL CLASSICAL-SOLUTIONS; EXPONENTIAL DECAY; SYSTEM; STABILITY; EXISTENCE;

D O I：

10.3934/krm.2012.5.583

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the large-time behavior of perturbative classical solutions to the hard and soft potential Boltzmann equation without the angular cut-off assumption in the whole space R-x(n) with n >= 3. We use the existence theory of global in time nearby Maxwellian solutions from [12, 11]. It has been a longstanding open problem to determine the large time decay rates for the soft potential Boltzmann equation in the whole space, with or without the angular cut-off assumption [26, 1]. For perturbative initial data, we prove that solutions converge to the global Maxwellian with the optimal large-time decay rate of O(t(-n/2+n/2r)) in the L-v(2)(L-x(r))-norm for any 2 <= r <= infinity.

引用

页码：583 / 613

页数：31