The generalized Constantin-Lax-Majda equation revisited
Marcus Wunsch · Communications in Mathematical Sciences · 2011
We continue our study of the generalized Constantin-Lax-Majda equation, which is an evolution equation in one space dimension modeling three-dimensional vorticity dynamics.First, we show that the BM O-norm of the vorticity controls the singularity formation for smooth solutions if the parameter a equals 2, and we proceed by demonstrating that there are small solutions which exist indefinitely in the presence of viscosity if a ≤ -2.