Math 712. Topics in Mathematical Physics: Fluid Mechanics
- Fall 18 - Hans Lindblad

The lectures are MW 1.30-2.45 in Gillman 77.
The course will cover local existence for a fluid with a free surface and global existence for the water wave problem. For the local existence we will follow Nordgren's thesis Well-posedness for the equations of motion of an inviscid, incompressible, self-gravitating fluid with free boundary. (dowloadable here). I will start with the introduction from Lindblad and Christodoulou On the motion of the free surface of liquid to explain the intuition (see also my talk). Next I will go on to doing the linearized energy estimates from Lindblad Well-posedness for the linearized motion of an incompressible liquid with free surface boundary. After that I will do the apriori bounds in the two dimensional case from Lindblad and Nordgren A priori estimates for the motion of a selfgravitating incompressible liquid with free surface boundary.

For the global existence we will follow a paper of Germain, Masmoudi and Shatah Global solutions for the gravity water waves equation in dimension 3 (dowloadable here). See also Ionescu, Pausader The Euler-Poisson system in 2D: Global stability of the constant equilibrium solution and Germain Space-time resonances and Putsateri, Shatah Space-time resonances and the null condition for (first order) systems of wave equations