On the Local Existence and Uniqueness for the 3D Euler Equation with a Free Interface

Igor Kukavica, Amjad Tuffaha, Vlad Vicol

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We address the local existence and uniqueness of solutions for the 3D Euler equations with a free interface. We prove the local well-posedness in the rotational case when the initial datum u0 satisfies u0∈ H2.5 + δ and [InlineEquation not available: see fulltext.], where δ> 0 is arbitrarily small, under the Taylor condition on the pressure.

Original languageEnglish (US)
Pages (from-to)535-563
Number of pages29
JournalApplied Mathematics and Optimization
Volume76
Issue number3
DOIs
StatePublished - Dec 1 2017

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Keywords

  • Cauchy invariance
  • Euler equations
  • Free surface
  • Local existence
  • Taylor condition
  • Waves

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