Existence for the -patch model and the QG sharp front in Sobolev spaces
Francisco Gancedo
Abstract
We consider a family of contour dynamics equations depending on a parameter with 0<α≤ 1. The vortex patch problem of the 2-D Euler equation is obtained taking α 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.
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