Existence result for heat-conducting viscous incompressible fluids with vacuum

초록

The Navier-Stokes system for heat-conducting incompressible fluids is studied in a domain Omega subset of 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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