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

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

2007-01-16

arxiv.org/abs/math/0701447v1

Mathematics

Analysis of PDEs

26 pages

Scientific paper

We consider a family of contour dynamics equations depending on a parameter
$\al$ with $0<\alpha\leq 1$. The vortex patch problem of the 2-D Euler equation
is obtained taking $\alpha\to 0$, and the case $\alpha=1$ 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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