Cheng Yu, Department of Mathematics, University of Texas at Austin, USA
Middle Lecture Room, Math Building
We will discuss recent results on the construction of weak solutions for 3D compressible Navier-Stokes equations with degenerate viscosities, including the construction of weak solutions for the viscous shallow water equation. This was proposed as an open problem by P.-L. Lions in his book on fluid mechanics in the late 90’. It has been solved, in collaboration with Alexis Vasseur, in our recent joint work. We will also mention some results on the energy conservation for the Navier-Stokes equations.