Global well-posedness of unsteady motion of viscous incompressible capillary liquid bounded by a free surface

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5 Citations (Scopus)

Abstract

In this paper, we prove the global well-posedness of free boundary problems of the Navier-Stokes equations in a bounded domain with surface tension. The velocity field is obtained in the Lp in time Lq in space maximal regularity class, (2<p<∞, N<q<∞, and 2/p+N/q<1), under the assumption that the initial domain is close to a ball and initial data are sufficiently small. The essential point of our approach is to drive the exponential decay theorem in the Lp-Lq framework for the linearized equations with the help of maximal Lp-Lq regularity theory for the Stokes equations with free boundary conditions and spectral analysis of the Stokes operator and the Laplace-Beltrami operator.

Original languageEnglish
Pages (from-to)117-152
Number of pages36
JournalEvolution Equations and Control Theory
Volume7
Issue number1
DOIs
Publication statusPublished - 2018

Keywords

  • Free boundary problems
  • Global well-posedness
  • Navier-stokes equations
  • Surface tension

ASJC Scopus subject areas

  • Modelling and Simulation
  • Control and Optimization
  • Applied Mathematics

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