Global regularity for the inhomogeneous incompressible Kelvin-Voigt Euler equations with vacuum

The Cauchy problem of the classical inhomogeneous incompressible Kelvin-Voigt Euler equations is investigated in this paper. More precisely, we prove the unique global strong solution with vacuum to this system in two, three and four space-dimensions. Our results are proved without any smallness on the initial data and without any regularity assumption on the initial density. Moreover, the initial density can contain vacuum states and even have compact support.