GLOBAL STRONG SOLUTION TO THE MULTIDIMENSIONAL INHOMOGENEOUS INCOMPRESSIBLE HEAT CONDUCTING NAVIER-STOKES FLOWS WITH VACUUM

摘要

We are concerned with the Cauchy problem of the multidimensional inhomogeneous incompressible heat conducting Navier-Stokes flows with fractional dissipation. We show that the problem admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states.