Communications in Mathematical Sciences

Volume 9 (2011)

Number 2

Critical thresholds in multi-dimensional restricted Euler equations

Pages: 583 – 596

DOI: http://dx.doi.org/10.4310/CMS.2011.v9.n2.a12

Author

Dongming Wei (Department of Mathematics, University of Wisconsin)

Abstract

Using the spectral dynamics, we study the critical threshold phenomena in the multidimensional restricted Euler (RE) equations. We identify sub-critical and sup-critical initial data for all space dimensions, which extends the previous result for the 3D and 4D restricted Euler equations. Our result suggests that: if the number of dimensions is odd, the finite time blowup is generic; in contrast, if the number of dimensions is even, there is a rich set of initial data which yields global smooth solutions.

Keywords

restricted Euler equations, critical thresholds, global regularity

2010 Mathematics Subject Classification

35B30, 35Q35

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