Self-similar solutions to the isothermal compressible Navier-Stokes equations |
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Authors: | Guo Zhenhua; Jiang Song |
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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
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Abstract: | ** Email: guo_zhenhua{at}iapcm.ac.cn*** Email: jiang{at}iapcm.ac.cn We investigate the self-similar solutions to the isothermalcompressible NavierStokes 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 Neas, J., Rika, M.& verák, V. (1996, On Leray's self-similar solutionsof the Navier-Stokes equations. Acta. Math., 176, 283294),and is consistent with the (unproved) existence of regular solutionsglobally in time for the compressible NavierStokes equations. |
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Keywords: | Self-similar solutions Isothermal compressible flows Navier-Stokes equations |
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