Cauchy problem for the Navier–Stokes–Voigt model governing nonhomogeneous flows - Antontsev, S. N. (2022)
The Navier-Stokes-Voigt model that governs flows with non-constant density of incompressible fluids with elastic properties is considered in the whole space domain R-d and in the entire time interval. If d is an element of{2,3,4}, we prove the existence of weak solutions (velocity, density and pressure) to the associated Cauchy problem. We also analyse some issues of regularity of the weak solutions to the considered problem and the large time behavior in special unbounded domains.