Gibbsian dynamics and ergodicity of magnetohydrodynamics and related systems forced by random noise

Research output: Contribution to journalArticlepeer-review

Abstract

The magnetohydrodynamics system consists of the Navier-Stokes equations from fluid mechanics, coupled with the Maxwell’s equations from electromagnetism through multiples of non-linear terms involving derivatives. Following the approach of [1], we prove the existence of a unique invariant measure in case the forcing terms consist of the cylindrical Wiener processes with only low modes. Its proof requires taking advantage of the structure of the non-linear terms carefully and is extended to various other related models such as the magnetohydrodynamics-Boussinesq system from fluid mechanics in atmosphere and oceans, as well as the magneto-micropolar fluid system from the theory of microfluids.

Original languageEnglish
Pages (from-to)412-444
Number of pages33
JournalStochastic Analysis and Applications
Volume37
Issue number3
DOIs
StatePublished - May 4 2019

Keywords

  • Boussinesq system
  • Navier-Stokes equations
  • ergodicity
  • magnetohydrodynamics
  • micropolar fluid

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