Strichartz estimates and local regularity for gravity-capillary water waves
Strichartz estimates and local regularity for gravity-capillary water waves
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Quang-Huy Nguyen , Princeton University
We will consider the water waves problem for 2D and 3D听 incompressible, irrotational, inviscid fluid flows subject to both听gravity and surface tension. The PDE is dispersive, quasilinear and听nonlocal. The questions on local existence and uniqueness in the听lowest regularity spaces are still in progress. We will discuss our听results on a blow-up criterion in terms of the Lipschitz norm of the听velocity; nonlinear Strichartz estimates for rough solutions; and听their application in estabishing a local well-posedness theory for听non-Lipschitz initial velocity.