Critical thresholds in multi-dimensional restricted Euler equations

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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Published 21 December 2010