On the Existence for the Free Interface 2D Euler Equation with a Localized Vorticity Condition

Igor Kukavica, Amjad Tuffaha, Vlad Vicol, Fei Wang

Research output: Contribution to journalArticle

Abstract

We prove a local-in-time existence of solutions result for the two dimensional incompressible Euler equations with a moving boundary, with no surface tension, under the Rayleigh–Taylor stability condition. The main feature of the result is a local regularity assumption on the initial vorticity, namely H1.5 + δ Sobolev regularity in the vicinity of the moving interface in addition to the global regularity assumption on the initial fluid velocity in the H2 + δ space. We use a special change of variables and derive a priori estimates, establishing the local-in-time existence in H2 + δ. The assumptions on the initial data constitute the minimal set of assumptions for the existence of solutions to the rotational flow problem to be established in 2D.

Original languageEnglish (US)
Pages (from-to)523-544
Number of pages22
JournalApplied Mathematics and Optimization
Volume73
Issue number3
DOIs
StatePublished - Jun 1 2016

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Rotational flow
Euler equations
Vorticity
Surface tension
Fluids
Existence of Solutions
Regularity
Incompressible Euler Equations
Moving Interface
Global Regularity
Moving Boundary
Change of Variables
Minimal Set
Surface Tension
Stability Condition
Fluid
Estimate

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

Cite this

On the Existence for the Free Interface 2D Euler Equation with a Localized Vorticity Condition. / Kukavica, Igor; Tuffaha, Amjad; Vicol, Vlad; Wang, Fei.

In: Applied Mathematics and Optimization, Vol. 73, No. 3, 01.06.2016, p. 523-544.

Research output: Contribution to journalArticle

Kukavica, Igor ; Tuffaha, Amjad ; Vicol, Vlad ; Wang, Fei. / On the Existence for the Free Interface 2D Euler Equation with a Localized Vorticity Condition. In: Applied Mathematics and Optimization. 2016 ; Vol. 73, No. 3. pp. 523-544.
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