2017/11/13 by Paicu, Marius, Zhang, Ping · 1 citation
#35Q30 #76D03 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1711.04490
In this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier-Stokes equations with viscous coefficient depending on the density and with initial density being discontinuous across some smooth interface. Compared with the previous results for the inhomogeneous Navier-Stokes equations with constant viscosity, the main difficulty here lies in the fact that the L1 in time Lipschitz estimate of the velocity field can not be obtained by energy method (see \citeDM17,LZ1, LZ2 for instance). Motivated by the key idea of Chemin to solve 2-D vortex patch of ideal fluid (\citeChemin91, Chemin93), namely, striated regularity can help to get the L^∞ boundedness of the double Riesz transform, we derive the \it a priori L1 in time Lipschitz estimate of the velocity field under the assumption that the viscous coefficient is close enough to a positive constant in the bounded function space. As an application, we shall prove the propagation of H3 regularity of the interface between fluids with different densities.