J. Korean Math. Soc. 2008; 45(3): 645-681
Printed May 1, 2008
Copyright © The Korean Mathematical Society.
Yonggeun Cho and Hyunseok Kim
Chonbuk National University, Sogang University
The Navier-Stokes system for heat-conducting incompressible fluids is studied in a domain $\Omega \subset \mathbf{R}^3$. 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
MSC numbers: Primary 35A05, 76D03
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