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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.
Applied Mathematics and Optimization – Springer Journals
Published: May 17, 2016
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