Seminar

Abstract: We introduce and analyse a fully-mixed formulation for the coupled problem arising in the interaction between a free fluid and a poroelastic medium. The flows in the free fluid and poroelastic regions are governed by the Navier-Stokes and Biot equations, respectively, and the transmission conditions are given by mass conservation, balance of stresses, and the Beavers-Joseph-Saffman law.

Abstract: In this talk, we will study the Cauchy problem for the Euler equations in vorticity form. With the initial data in L^1∩L^∞, the uniqueness of the solution is guaranteed by Yudovich's classic result. However, it is a long-standing open question if it is possible to extend the result to the L^p scale. We will disprove it by constructing a one-parameter family of solutions with the same initial data and external force.