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

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09079
 Bibcode:
 2021arXiv211009079C
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics
 EPrint:
 33 pages, 1 figure