Conservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids

Abstract

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.

Keywords:

• Incompressible Euler system
• Lifespan
• Striated and conormal regularity
• Variable density

Mathematics Subject Classification:

• 35Q31
• 76B03
• 35B65