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# Existence result for heat-conducting viscous incompressible fluids with vacuum

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 Title: Existence result for heat-conducting viscous incompressible fluids with vacuum Authors: Cho, Yonggeun Browse this author Kim, Hyunseok Browse this author Keywords: heat-conducting incompressible Navier-Stokes equations strong solutions vacuum Issue Date: 2005 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 742 Start Page: 1 End Page: 47 Abstract: We study the Navier-Stokes equations for heat-conducting incompressible fluids in a domain $\Omega \subset \mathbf{R}^3$ whose viscosity, heat conduction coefficients and specific heat at constant volume are in general functions of density and temperature. We prove the local existence of the unique strong solution, provided the initial data satisfy a natural compatibility condition. For the strong regularity, we do not assume the positivity of initial density; it may vanish in an open subset (vacuum) of $\Omega$ or decay at infinity when $\Omega$ is unbounded. Type: bulletin (article) URI: http://hdl.handle.net/2115/69550 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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