In this paper we construct families of real analytic solutions of the Surface Quasi-Geostrophic equation (SQG) that are locally constant outside a thin neighborhood of a curve of arbitrarily small thickness. Despite the fact that only local existence results are known for SQG, and that our initial conditions have a arbitrarily large gradient we show that solutions exist for a time independent of the thickness of the neighborhood.
|Original language||English (US)|
|Number of pages||40|
|Journal||Archive for Rational Mechanics and Analysis|
|State||Published - Oct 27 2015|
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)
- Mechanical Engineering