Solvability of the initial value problem to a model system for water waves

Yuuta Murakami, Tatsuo Iguchi

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider the initial value problem to a model system for water waves. The model system is the Euler–Lagrange equations for an approximate Lagrangian which is derived from Luke’s Lagrangian for water waves by approximating the velocity potential in the Lagrangian. The model are nonlinear dispersive equations and the hypersurface t = 0 is characteristic for the model equations. Therefore, the initial data have to be restricted in an infinite dimensional manifold in order to the existence of the solution. Under this necessary condition and a sign condition, which corresponds to a generalized Rayleigh–Taylor sign condition for water waves, on the initial data, we show that the initial value problem is solvable locally in time in Sobolev spaces.

Original language English 470-491 22 Kodai Mathematical Journal 38 2 https://doi.org/10.2996/kmj/1436403901 Published - 2015 Jul 11

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Water Waves
Initial Value Problem
Solvability
Nonlinear Dispersive Equations
Euler-Lagrange Equations
Model
Sobolev Spaces
Hypersurface
Necessary Conditions

Keywords

• Luke’s lagrangian
• Shallow water
• Water waves

ASJC Scopus subject areas

• Mathematics(all)

Cite this

In: Kodai Mathematical Journal, Vol. 38, No. 2, 11.07.2015, p. 470-491.

Research output: Contribution to journalArticle

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