Abstract
We investigate the (slightly) super-critical two-dimensional Euler equations. The paper consists of two parts. In the first part we prove well-posedness in Cs spaces for all s > 0. We also give growth estimates for the Cs norms of the vorticity for 0 < s ≦ 1. In the second part we prove global regularity for the vortex patch problem in the super-critical regime. This paper extends the results of Chae et al. where they prove well-posedness for the so-called LogLog-Euler equation. We also extend the classical results of Chemin and Bertozzi-Constantin on the vortex patch problem to the slightly supercritical case. Both problems we study in the setting of the whole space.
Original language | English (US) |
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Pages (from-to) | 965-990 |
Number of pages | 26 |
Journal | Archive for Rational Mechanics and Analysis |
Volume | 211 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2014 |
All Science Journal Classification (ASJC) codes
- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering