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Conservation of geometric structures for non-homogeneous inviscid incompressible fluids

Abstract : We obtain a result about propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension N =2. In particular, we investigate conservation of striated and conormal regularity, which is a natural way of generalizing the 2-D structure of vortex patches. The results we get are only local in time, even in the dimension N=2; however, we provide an explicit lower bound for the lifespan of the solution. In the case of physical dimension N=2 or 3, we investigate also propagation of Hölder regularity in the interior of a bounded domain.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00733562
Contributor : Francesco Fanelli <>
Submitted on : Tuesday, September 18, 2012 - 10:52:00 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

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  • HAL Id : hal-00733562, version 1

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Francesco Fanelli. Conservation of geometric structures for non-homogeneous inviscid incompressible fluids. Communications in Partial Differential Equations, Taylor & Francis, 2012, 37 (9), pp.1553-1595. ⟨hal-00733562⟩

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