EXISTENCE RESULT FOR HEAT-CONDUCTING VISCOUS INCOMPRESSIBLE FLUIDS WITH VACUUM

EXISTENCE RESULT FOR HEAT-CONDUCTING VISCOUS INCOMPRESSIBLE FLUIDS WITH VACUUM

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...

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Veröffentlicht in:Journal of the Korean Mathematical Society 2008, Vol.45 (3), p.645-681
Hauptverfasser: Cho, Yong-Geun, Kim, Hyun-Seok
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container_title Journal of the Korean Mathematical Society
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creator Cho, Yong-Geun
Kim, Hyun-Seok
description 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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title EXISTENCE RESULT FOR HEAT-CONDUCTING VISCOUS INCOMPRESSIBLE FLUIDS WITH VACUUM
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