Blow up of classical solutions to the isentropic compressible Navier–Stokes equations |
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| Institution: | 1. LAMA UMR5127 CNRS, Université de Savoie Mont-Blanc, 73376 Le Bourget du Lac, France;2. Fondation Mathématique Jacques Hadamard and CMLA ENS Cachan, 94235 Cachan Cedex, France;3. Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau Cedex, France;4. Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warszawa, Poland;5. Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland;1. Laboratoire de Mathématiques, CNRS UMR 5127, Université de Savoie, 73376 Le Bourget-du-Lac, France;2. Laboratoire de Mathématiques, CNRS UMR 8524, Université de Lille 1, Villeneuve d’Ascq, France;1. College of Mathematics and Computational Science, Shenzhen University, China;2. Department of Mathematics, Capital Normal University, Beijing, China |
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| Abstract: | In this work we consider the isentropic compressible Navier–Stokes equations in three space dimensions. Blow up result will be established, assuming the gradient of the velocity satisfies some decay constraint and the initial total momentum does not vanish. We prove the main result by a contradiction argument, based on the conservation of the total mass and the total momentum. |
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| Keywords: | Blow up Isentropic Compressible Navier–Stokes equations |
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