On the Linear Stability of Vortex Columns in the Energy Space

  • Thierry Gallay
  • Didier SmetsEmail author


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 our previous work Gallay and Smets (Spectral stability of inviscid columnar vortices, 2018. arXiv:1805.05064), where spectral stability was established for the linearized operator in the enstrophy space.



This work was partially supported by grants ANR-18-CE40-0027 (Th.G.) and ANR-14-CE25-0009-01 (D.S.) from the “Agence Nationale de la Recherche”. The authors warmly thank an anonymous referee for suggesting a more natural way to prove compactness of the operator \(B_{m,k}\), which is now implemented in Sect. 3.2.

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Conflict of interest

The author(s) declares that they have no competing interests.


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Authors and Affiliations

  1. 1.Institut FourierUniversité Grenoble AlpesCNRSGièresFrance
  2. 2.Laboratoire Jacques-Louis LionsSorbonne UniversitéParisFrance

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