English

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

Analysis of PDEs 2015-05-19 v2

Abstract

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][0,{T}/\eps] for some \eps\eps independent of constant T.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.

Keywords

Cite

@article{arxiv.1008.1391,
  title  = {Large time wellposdness to the 3-D Capillary-Gravity Waves in the long wave regime},
  author = {Mei Ming and Ping Zhang and Zhifei Zhang},
  journal= {arXiv preprint arXiv:1008.1391},
  year   = {2015}
}

Comments

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