Two-phase problem for two-dimensional water waves of finite depth

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider the two-phase problem for two-dimensional and irrotational motion of incompressible ideal fluids in the case that the fluids are separated into the lower and the upper parts by an almost horizontal interface and that there is an almost flat bottom below the lower fluid. It is proved that the Cauchy problem is well-posed, locally in time, in a Sobolev space of finite smoothness, if the surface tension is taken into account and the initial data are suitably close to the equilibrium rest state. The main part of the proof is the reduction of the problem to a quasi-linear system of integro-differential equations for the function defining the interface and the horizontal component of the velocity of the lower fluid on the interface.

Original languageEnglish
Pages (from-to)791-821
Number of pages31
JournalMathematical Models and Methods in Applied Sciences
Volume7
Issue number6
Publication statusPublished - 1997 Sep
Externally publishedYes

Fingerprint

Water waves
Water Waves
Fluid
Fluids
Horizontal
Quasilinear System
Ideal Fluid
Surface Tension
Integro-differential Equation
Incompressible Fluid
Sobolev spaces
Sobolev Spaces
Integrodifferential equations
Smoothness
Cauchy Problem
Linear systems
Surface tension
Motion

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Modelling and Simulation

Cite this

Two-phase problem for two-dimensional water waves of finite depth. / Iguchi, Tatsuo.

In: Mathematical Models and Methods in Applied Sciences, Vol. 7, No. 6, 09.1997, p. 791-821.

Research output: Contribution to journalArticle

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