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

On the Local Existence and Uniqueness for the 3D Euler Equation with a Free Interface 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 $$u_0$$ u 0 satisfies $$u_0\in H^{2.5+\delta }$$ u 0 ∈ H 2.5 + δ and [InlineEquation not available: see fulltext.], where $$\delta >0$$ δ > 0 is arbitrarily small, under the Taylor condition on the pressure. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

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

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References (56)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-016-9360-6
Publisher site
See Article on Publisher Site

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 $$u_0$$ u 0 satisfies $$u_0\in H^{2.5+\delta }$$ u 0 ∈ H 2.5 + δ and [InlineEquation not available: see fulltext.], where $$\delta >0$$ δ > 0 is arbitrarily small, under the Taylor condition on the pressure.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: May 17, 2016

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