Well-posedness in Sobolev spaces of the full water wave problem in 3-D

Journal of the American Mathematical Society - Tập 12 Số 2 - Trang 445-495
Sijue Wu1,2
1Department of Mathematics, The University of Iowa, Iowa City, Iowa, 52242
2Department of Mathematics, University of Maryland, College Park, Maryland, 20742

Tóm tắt

We consider the motion of the interface of a 3-D inviscid, incompressible, irrotational water wave, with air region above water region and surface tension zero. We prove that the motion of the interface of the water wave is not subject to Taylor instability, as long as the interface separates the whole 3-D space into two simply connected C 2 C^{2} regions. We prove further the existence and uniqueness of solutions of the full 3-D water wave problem, locally in time, for any initial interface that separates the whole 3-D space into two simply connected regions.

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