In this paper, we study the singular vortex patches in the two-dimensional incompressible Navier-Stokes equations. We show, in particular, that if the initial vortex patch is C1+s outside a singular set ∑, so the velocity is, for all time, lipschitzian outside the image of ∑ through the viscous flow. In addition, the correponding lipschitzian norm is independant of the viscosity. This allows us to prove some results related to the inviscid limit for the geometric structures of the vortex patch.
- Inviscid limit
- Littlewood-Paley theory
- Navier-Stokes and Euler equations
- Singular vortex patches
ASJC Scopus subject areas