Global strong solution to the multidimensional inhomogeneous incompressible heat conducting Navier–Stokes flows with vacuum

Abstract

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.