Flexibility and Rigidity in Steady Fluid Motion

Peter Constantin, Theodore D. Drivas, Daniel Ginsberg

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable steady solutions with no stagnation points occupying a two-dimensional periodic channel, or axisymmetric solutions in (hollowed out) cylinder, must have certain structural symmetries. It is additionally shown that such solutions can be deformed to occupy domains which are themselves small perturbations of the base domain. As application of the general scheme, Arnol’d stable solutions are shown to be structurally stable.

Original languageEnglish (US)
JournalCommunications In Mathematical Physics
DOIs
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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