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The global wellposedness of the 3D heat-conducting viscous incompressible fluids with bounded density
Institution:1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, China;2. Department of Mathematics, Sichuan University, Chengdu, Sichuan 610021, China;1. Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China;2. School of Science, Hubei University of Technology, Wuhan 430068, China;1. Deutsches Zentrum für Luft- und Raumfahrt (DLR), Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany;2. NASA Goddard Space Flight Center, Greenbelt, MD, USA;3. STARSS II Affiliate, NASA Langley Research Center, Hampton, VA, USA;1. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Republic of Singapore;2. Department of Mathematics, Beijing Institute of Technology, Beijing 100081, People’s Republic of China
Abstract:We consider the global wellposedness of the inhomogeneous incompressible heat-conducting viscous fluids in three dimension space. We generalize the result of Fujita & Kato for Navier–Stokes to the heat-conducting inhomogeneous incompressible viscous fluids. The key point is that we get the global wellposedness under the assumption that the initial density has positive lower and upper bound and the initial temperature can be arbitrarily large.
Keywords:Inhomogeneous incompressible fluids  Optimal decay rates  Energy method  Sobolev interpolation  Heat conducting
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