English

On the linear stability of vortex columns in the energy space

Analysis of PDEs 2019-10-02 v2

Abstract

We investigate the linear stability of inviscid columnar vortices with respect to finite energy perturbations. For a large class of vortex profiles, we show that the linearized evolution group has a sub-exponential growth in time, which means that the associated growth bound is equal to zero. This implies in particular that the spectrum of the linearized operator is entirely contained in the imaginary axis. This contribution complements the results of a previous work, where spectral stability was established for the linearized operator in the enstrophy space.

Keywords

Cite

@article{arxiv.1811.07584,
  title  = {On the linear stability of vortex columns in the energy space},
  author = {Thierry Gallay and Didier Smets},
  journal= {arXiv preprint arXiv:1811.07584},
  year   = {2019}
}

Comments

Major revision, including a complete rewriting of Section 3