Third order semilinear dispersive equations related to deep water waves
Hiroyuki Chihara
Abstract
We present local existence theorem of the initial value problem for third order semilinear dispersive partial differential equations in two space dimensions. This type of equations arises in the study of gravity wave of deep water, and cannot be solved by the classical energy method. To solve the initial value problem, we make full use of pseudodifferential operators with nonsmooth coefficients.
Create a lesson
Related papers
A Riesz-Map Preconditioned Extragradient Method for Price Formation in Mean Field Games
Yeva Gevorgyan, Diogo Gomes
An Aleksandrov estimate for kinetic equations with rough coefficients
Amĺie Loher, Connor Mooney, Clément Mouhot et al.
The Inviscid Limit in Uniformly Local Yudovich Spaces
Zachary Radke
Ground states and sharp logarithmic Sobolev inequalities for logarithmic Schrödinger equations with partial confinement
Baihong Li, Jarosław Mederski, Xiangjian Zeng
Existence and large-field asymptotics of Hopfions in a continuum model of frustrated magnets
Glal Bacho, Christof Melcher
Existence and uniqueness of bound states with prescribed number of nodes for nonlinear dispersive equations on spherically symmetric manifolds
Valentino Badalucco