Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2008.05.31
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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.

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References

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