On the 2D free boundary Euler equation

Igor Kukavica; Amjad Tuffaha

doi:10.3934/eect.2012.1.297

Article Contents

2012, Volume 1, Issue 2: 297-314. Doi: 10.3934/eect.2012.1.297

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On the 2D free boundary Euler equation

Igor Kukavica^1, and
Amjad Tuffaha^2,

1.
Department of Mathematics, University of Southern California, Los Angeles, CA 90089
2.
Department of Mathematics, The Petroleum Institute, Abu Dhabi

Received: April 30, 2012

Revised: June 30, 2012

Published: November 2012

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Abstract

We provide a new simple proof of local-in-time existence of regular solutions to the Euler equation on a domain with a free moving boundary and without surface tension in 2 space dimensions. We prove the existence under the condition that the initial velocity belongs to the Sobolev space $H^{2.5+δ}$ where $\delta>0$ is arbitrary.

Keywords:

Free moving boundary problem,
surface water waves,
shallow water,
incompressible inviscid flow,
free boundary euler equations with no surface tension.

Mathematics Subject Classification: Primary: 35Q31, 74J15; Secondary: 35R37.

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