Global regularities of 2D density patch problem for inhomogeneous incompressible viscous flow

In this talk I will consider the density patch problem for the two dimensional inhomogeneous incompressible viscous flow. I will show that the Besov regularities as well as the tangential regularities of any order for the velocity field can be propagated globally in time. The proof relies on the (time weighted) energy estimates. This is a joint work with Ping Zhang from Beijing.