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

Francisco Gancedo
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Abstract

We 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.

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Francisco Gancedo. 2007-01-16. Existence for the $\al$-patch model and the QG sharp front in Sobolev spaces. https://arxiv.org/abs/math/0701447

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