Asymptotic profiles for the compressible Navier-Stokes equations in the whole space

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• 作者：Yoshiyuki Kagei^a ; Masatoshi Okita^b ; ^{m-okita@kurume-nct.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Compressible Navier&ndash ; Stokes equations ; Asymptotic profiles ; Convergence rate
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：297-317
• 全文大小：375 K

文摘

This paper is concerned with the large time behavior of strong solutions of the compressible Navier–Stokes equation in the whole space class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303481&_mathId=si1.gif&_user=111111111&_pii=S0022247X16303481&_rdoc=1&_issn=0022247X&md5=edaf5625ddc378c21d5c8158d235767f" title="Click to view the MathML source">Rⁿ(n≥3)class="mathContainer hidden">class="mathCode">${\mathbb{R}}^n(n\ge 3)$ around the constant state. It was shown by Kawashima, Matsumura and Nishida (1979) and Hoff and Zumbrun (1995) that the perturbation of the constant state is time-asymptotic to a solution of the linearized problem, that is, a first-order asymptotic profile. In this paper a second-order asymptotic profile of the solution, which is caused by the nonlinear effect, is given.