In this article we get a result on 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 generalize the 2-D structure of vortex patches. The results we get are only local in time, even for 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.

%B Communications in Partial Differential Equations %I Taylor & Francis %V 37 %P 1553-1595 %G eng %U https://doi.org/10.1080/03605302.2012.698343 %R 10.1080/03605302.2012.698343