Decay estimates for isentropic compressible Navier¨CStokes equations in bounded domain

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• 作者：Daoyuan  ; Fang ;   ; ^{dyf@zju.edu.cn} ; Ruizhao  ; Zi ;   ; ^{ruizhao3805@163.com} ; Ting  ; Zhang ;   ; ^{zhangting79@zju.edu.cn}
• 关键词：Compressible Navier&ndash ; Stokes equations ; Decay estimates
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 出版时间：15 February 2012
• 年：2012
• 卷：386
• 期：2
• 页码：939-947
• 全文大小：165 K

文摘

In this paper, under the hypothesis that ¦Ñ is upper bounded, we construct a Lyapunov functional for the multidimensional isentropic compressible Navier¨CStokes equations and show that the weak solutions decay exponentially to the equilibrium state in norm. This can be regarded as a generalization of Matsumura and Nishida?s results [A. Matsumura, T. Nishida, in: Computing Methods in Applied Sciences and Engineering, vol. V, 1982, pp. 389?06], since our analysis is done in the framework of Lions [P.-L. Lions, Oxford Science Publication, 1998] and Feireisl et al. [E. Fereisl, A. Novotny, H. Petzeltov¨¢, J. Math. Fluid Mech. 3 (2001) 358?92], the higher regularity of and the uniformly positive lower bound of ¦Ñ are not necessary in our analysis and vacuum may be admitted. Indeed, the upper bound of the density ¦Ñ plays the essential role in our proof.