Self-similar solutions to the isothermal compressible Navier-Stokes equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Self-similar solutions to the isothermal compressible Navier-Stokes equations

Authors:	Guo Zhenhua; Jiang Song

Institution:	¹ Laboratory of Nonlinear Analysis, Department of Mathematics, Huazhong Normal University, Wuhan 430079, China and LCP, Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, China, ² LCP, Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, China

Abstract:	^ Email: guo_zhenhua{at}iapcm.ac.cn^* Email: jiang{at}iapcm.ac.cn We investigate the self-similar solutions to the isothermalcompressible Navier–Stokes equations. The aim of thispaper is to show that there exist neither forward nor backwardself-similar solutions with finite total energy. This generalizesthe results for the incompressible case in Ne $c$ as, J., R ${udot}$ $z$ i $c$ ka, M.& $S$ verák, V. (1996, On Leray's self-similar solutionsof the Navier-Stokes equations. Acta. Math., 176, 283–294),and is consistent with the (unproved) existence of regular solutionsglobally in time for the compressible Navier–Stokes equations.

Keywords:	Self-similar solutions Isothermal compressible flows Navier-Stokes equations
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