On vortex stretching for anti-parallel axisymmetric flows

Abstract

We consider axisymmetric incompressible inviscid flows without swirl in ${\mathbb{R}}^3$, under the assumption that the axial vorticity is non-positive in the upper half space and odd in the last coordinate, which corresponds to the flow setup for head-on collision of anti-parallel vortex rings. For any such data, we establish monotonicity and infinite growth of the vorticity impulse on the upper half-space. As an application, we achieve infinite growth of Sobolev norms for certain classical/smooth and compactly supported vorticity solutions in ${\mathbb{R}}^3$.

33 pages, 1 figure; several results have been improved from the previous version

References in corpus (1)

• Infinite superlinear growth of the gradient for the two-dimensional Euler equation

Cited by in corpus (1)

• Finite-time blowup for the inviscid vortex stretching equation