Compressible fluids and active potentials |
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| Institution: | 1. Department of Mathematics, Princeton University, Princeton, NJ 08544, United States of America;2. DPMMS, University of Cambridge, Cambridge CB3 0WA, United Kingdom;1. Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom;2. Department of Mathematics, Yonsei University, Seoul 03722, Republic of Korea;1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA;2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;3. Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China;4. School of Mathematical Sciences, Beijing Normal University and Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China |
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| Abstract: | We consider a class of one dimensional compressible systems with degenerate diffusion coefficients. We establish the fact that the solutions remain smooth as long as the diffusion coefficients do not vanish, and give local and global existence results. The models include the barotropic compressible Navier-Stokes equations, shallow water systems and the lubrication approximation of slender jets. In all these models the momentum equation is forced by the gradient of a solution-dependent potential: the active potential. The method of proof uses the Bresch-Desjardins entropy and the analysis of the evolution of the active potential. |
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| Keywords: | Compressible flow Shallow water Slender jet Global existence |
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