Remarks on the Blow-up of the Euler Equations and the Related Equations

Abstract

We consider the Euler system for inviscid incompressible fluid flows, and its perturbations in ℝn, n≥2. We prove global well-posedness of this perturbed Euler system in the Triebel-Lizorkin spaces for initial vorticity which is small in the critical Besov norms. Comparison type theorems about the blow-up of solutions are proved between the Euler system and its perturbations. We also study the possiblity of the self-similar type of blow-up of solutions to the equations.