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

DOI 7 Citations Open Access
  • Murakami Yuuta
    Department of Mathematics Faculty of Science and Technology, Keio University
  • Iguchi Tatsuo
    Department of Mathematics Faculty of Science and Technology, Keio University

Search this article

Description

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.

Journal

  • Kodai Mathematical Journal

    Kodai Mathematical Journal 38 (2), 470-491, 2015

    Institute of Science Tokyo, Department of Mathematics

Citations (7)*help

See more

Keywords

Details 詳細情報について

  • CRID
    1390282680250962816
  • NII Article ID
    130005475910
  • DOI
    10.2996/kmj/1436403901
  • ISSN
    18815472
    03865991
  • Text Lang
    en
  • Data Source
    • JaLC
    • Crossref
    • CiNii Articles
    • OpenAIRE
  • Abstract License Flag
    Disallowed

Report a problem

Back to top