Global well-posedness of the 3-D full water wave problem

Details Global well-posedness of the 3-D full water wave problem Global well-posedness of the 3-D full water wave problem

2009-10-13

arxiv.org/abs/0910.2473v1

Mathematics

Analysis of PDEs

60 pages

Scientific paper

We consider the problem of global in time existence and uniqueness of solutions of the 3-D infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For any initial interface that is sufficiently small in its steepness and velocity, we show that there exists a unique smooth solution of the full water wave problem for all time, and the solution decays at the rate $1/t$.

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