Global well-posedness of the 2D incompressible Navier–Stokes equations with density-dependent viscosity coefficient. (December 2020) - Liu, Yang
Abstract: This paper deals with the 2D incompressible Navier–Stokes equations with density-dependent viscosity over bounded domains. The global existence of strong solutions is established in the vacuum cases, provided the assumption that the bound of density is suitably small, which is in sharp contrast to the recent work (Huang and Wang, 2014), where the smallness assumption on ‖ ∇ μ ( ρ 0 ) ‖ L q ( q > 2 ) is needed. Furthermore, we also obtain the exponential decay rates of the spatial gradients of the velocity and the pressure.