EXISTENCE RESULT FOR HEAT-CONDUCTING VISCOUS INCOMPRESSIBLE FLUIDS WITH VACUUM

Yong-Geun Cho, Hyun-Seok Kim
2008 Journal of the Korean Mathematical Society  
We study the Navier-Stokes equations for heat-conducting incompressible fluids in a domain Ω ⊂ R 3 whose viscosity, heat conduction coefficients and specific heat at constant volume are in general functions of density and temperature. We prove the 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 Ω or decay
more » ... um) of Ω or decay at infinity when Ω is unbounded.
doi:10.4134/jkms.2008.45.3.645 fatcat:nrvun4ko2vbwbm22qzaorj4t7e