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arXiv · 1305.1128

Conservation of geometric structures for non-homogeneous inviscid incompressible fluids

Francesco Fanelli
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Abstract

We obtain a result about propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension $N\geq2$. 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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Francesco Fanelli. 2013-05-06. Conservation of geometric structures for non-homogeneous inviscid incompressible fluids. https://arxiv.org/abs/1305.1128

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