### 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