Analysis Seminar

We address the local existence of solutions for the water wave problem, which is modeled by the incompressible Euler equations in a domain with an evolving boundary. We are particularly interested in the local existence for the initial velocity, which is rotational and belongs to a low regularity Sobolev space. We will review the available existence and uniqueness results for the problem with surface tension. We will also briefly mention the compressible case and discuss some other free-boundary problems. The results are joint with M. Disconzi and A. Tuffaha.