Existence for the $\al$-patch model and the QG sharp front in Sobolev spaces

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122057We consider a family of contour dynamics equations depending on a parameter $\al$ with $0<α\leq 1$. The vortex patch problem of the 2-D Euler equation is obtained taking $α\to 0$, and the case $α=1$ corresponds to a sharp front of the QG equation. We prove local-in-time existence for the family of equations in Sobolev spaces.26 pagesAnalysis of PDEsExistence for the $\al$-patch model and the QG sharp front in Sobolev spacestext