Acoustic limit for the Boltzmann equation in the whole space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:367

Article

Liu, Shuangqian

关键词: Acoustic limit;    Boltzmann equation;    Landau equation;    Cauchy problem;   

DOI  :  10.1016/j.jmaa.2009.12.015

来源: Elsevier

【 摘 要 】

This paper is devoted to the following rescaled Boltzmann equation in the acoustic time scaling in the whole space partial derivative(t)F(epsilon) + v.del(x)F(epsilon) = 1/epsilon Q(F(epsilon), F(epsilon)), x epsilon R(3), t < 0, (0.1) with prescribed initial data F(epsilon)vertical bar(r=0) = F(epsilon)(0,x,v), x epsilon R(3). For a solution F(epsilon) (t, x, v) = mu + root mu epsilon f(epsilon) (t, x, v) to the rescaled Boltzmann equation (0.1) in the whole space R(3) for all t >= 0 with initial data F(epsilon)(0, x, v) = F(0)(epsilon)(x, v) = mu + root mu epsilon f(epsilon) (0, x, v), x, v epsilon R(3), our main purpose is to justify the global-in-time uniform energy estimates of f(epsilon)(t, x, v) in c and prove that f(epsilon)(t, x, v) converges strongly to f (t, x, v) whose dynamic is governed by the acoustic system. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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