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

Igor Kukavica; Amjad Tuffaha; Vlad Vicol

doi:10.1007/s00245-016-9360-6

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

Igor Kukavica, Amjad Tuffaha, Vlad Vicol

Mathematics

Research output: Contribution to journal › Article › peer-review

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∈ H^2.5 ⁺ ^δ and [InlineEquation not available: see fulltext.], where δ> 0 is arbitrarily small, under the Taylor condition on the pressure.

Original language	English (US)
Pages (from-to)	535-563
Number of pages	29
Journal	Applied Mathematics and Optimization
Volume	76
Issue number	3
DOIs	https://doi.org/10.1007/s00245-016-9360-6
State	Published - Dec 1 2017

Keywords

Cauchy invariance
Euler equations
Free surface
Local existence
Taylor condition
Waves

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

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10.1007/s00245-016-9360-6

Cite this

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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.",

keywords = "Cauchy invariance, Euler equations, Free surface, Local existence, Taylor condition, Waves",

author = "Igor Kukavica and Amjad Tuffaha and Vlad Vicol",

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AB - 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.

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KW - Free surface

KW - Local existence

KW - Taylor condition

KW - Waves

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

Abstract

Keywords

ASJC Scopus subject areas

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