Communications in Mathematical Sciences
Volume 9 (2011)
Critical thresholds in multi-dimensional restricted Euler equations
Pages: 583 – 596
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.
restricted Euler equations, critical thresholds, global regularity
2010 Mathematics Subject Classification