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http://dx.doi.org/10.4134/JKMS.2008.45.3.645

EXISTENCE RESULT FOR HEAT-CONDUCTING VISCOUS INCOMPRESSIBLE FLUIDS WITH VACUUM  

Cho, Yong-Geun (Department of Mathematics, and Institute of Pure and Applied Mathematics Chonbuk National University)
Kim, Hyun-Seok (Department of Mathematics Sogang University)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.3, 2008 , pp. 645-681 More about this Journal
Abstract
The Navier-Stokes system for heat-conducting incompressible fluids is studied in a domain ${\Omega}{\subset}R^3$. The viscosity, heat conduction coefficients and specific heat at constant volume are allowed to depend smoothly on density and temperature. We prove 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.
Keywords
heat-conducting incompressible Navier-Stokes equations; strong solutions; vacuum;
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