Striated Regualrity of 2-D inhomogeneous incompressible Navier-Stokes system with variable viscosity
Salle de Conférences
le 02 octobre 2018 à 11:30
In this talk, we shall 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
in time Lipschitz estimate of the velocity field can not be obtained by energy method. Motivated by the key idea of Chemin to solve 2-D vortex patch of ideal fluid, namely, striated regularity can help to get the
boundedness of the double Riesz transform, we derive the a priori
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
regularity of the interface between fluids with different densities. This is a joint work with Marius Paicu.