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- Title
Large Time Well-posedness of the Three-Dimensional Capillary-Gravity Waves in the Long Wave Regime.
- Authors
Ming, Mei; Zhang, Ping; Zhang, Zhifei
- Abstract
In the regime of weakly transverse long waves, given long-wave initial data, we prove that a non-dimensionalized water wave system in an infinite strip under the influence of gravity and surface tension on the upper free interface has a unique solution on [ $${0, T/ \varepsilon}$$ ] for some $${\varepsilon}$$ independent of constant T. We shall prove in the subsequent paper (Ming et al., The long wave approximation to the three-dimensional capillary gravity waves, ) that on the same time interval, these solutions can be accurately approximated by sums of solutions of two decoupled Kadomtsev-Petviashvili (KP) equations.
- Subjects
DIMENSIONAL analysis; SHEAR waves; MATHEMATICAL proofs; GRAVITY; SURFACE tension; APPROXIMATION theory; NUMERICAL solutions to differential equations; MATHEMATICAL analysis
- Publication
Archive for Rational Mechanics & Analysis, 2012, Vol 204, Issue 2, p387
- ISSN
0003-9527
- Publication type
Article
- DOI
10.1007/s00205-011-0479-y