Local well-posedness of free surface problems for the navier-stokes equations in a general domain

Yoshihiro Shibata*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

In this paper, we prove the local well-posedness of the free boundary problems of Navier-Stokes equations in a general domain RN (N 2). The velocity field is obtained in the maximal regularity class W2;1 q;p (0 T)) = Lp((0; T);Wq ()N) W1 p ((0; T);Lq()N) (2< 1 and N < q < 1) for any initial data satisfying certain compatibility conditions. The assumption of the domain is the unique existence of solutions to the weak Dirichlet-Neumann problem as well as some uniformity of covering of the closure of. A bounded domain, a perturbed half space, and a perturbed layer satisfy the conditions for the domain, and therefore drop problems and ocean problems are treated in the uniform manner. Our method is based on the maximal Lp-Lq regularity theorem of a linearized problem in a general domain.

Original languageEnglish
Pages (from-to)315-342
Number of pages28
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume9
Issue number1
DOIs
Publication statusPublished - 2016 Feb

Keywords

  • Free boundary problems
  • Gravity force
  • Local well-posedness
  • Navier-Stokes equations
  • Surface tension

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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