Large time wellposdness to the 3-D Capillary-Gravity Waves in the long wave regime

Details Large time wellposdness to the 3-D Capillary-Gravity Waves in the long wave regime Large time wellposdness to the 3-D Capillary-Gravity Waves in the long wave regime

2010-08-08

arxiv.org/abs/1008.1391v2

Mathematics

Analysis of PDEs

Split the original paper(The long wave approximation to the 3-D capillary-gravity waves) into two parts, this is the first one

Scientific paper

In the regime of weakly transverse long waves, given long-wave initial data, we prove that the nondimensionalized water wave system in an infinite strip under influence of gravity and surface tension on the upper free interface has a unique solution on $[0,{T}/\eps]$ for some $\eps$ independent of constant $T.$ We shall prove in the subsequent paper \cite{MZZ2} that on the same time interval, these solutions can be accurately approximated by sums of solutions of two decoupled Kadomtsev-Petviashvili (KP) equations.

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