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June 2015 Solvability of the initial value problem to a model system for water waves
Yuuta Murakami, Tatsuo Iguchi
Kodai Math. J. 38(2): 470-491 (June 2015). DOI: 10.2996/kmj/1436403901

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.

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Yuuta Murakami. Tatsuo Iguchi. "Solvability of the initial value problem to a model system for water waves." Kodai Math. J. 38 (2) 470 - 491, June 2015. https://doi.org/10.2996/kmj/1436403901

Information

Published: June 2015
First available in Project Euclid: 9 July 2015

zbMATH: 1328.35175
MathSciNet: MR3368076
Digital Object Identifier: 10.2996/kmj/1436403901

Rights: Copyright © 2015 Tokyo Institute of Technology, Department of Mathematics

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Vol.38 • No. 2 • June 2015
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