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 $N\ge 2$. 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.

References in corpus (1)

• On the well-posedness of the incompressible density-dependent Euler equations in the $L^p$ framework