Strong Feller property of the magnetohydrodynamics system forced by space-time white noise

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Abstract

The magnetohydrodynamics system forced by space-time white noise has been proposed and investigated by physicists and engineers, although without rigorous mathematical proofs of its solution's fundamental properties. Applying the theory of regularity structures, we prove its well-posedness and strong Feller property. The proof requires a careful treatment of nonlinear terms which are sensitive to specific components of the solution that is a six-dimensional vector field, of which the first three and the last three are velocity and magnetic fields, respectively.

Original languageEnglish
Pages (from-to)4373-4463
Number of pages91
JournalNonlinearity
Volume34
Issue number6
DOIs
StatePublished - Jun 2021

Keywords

  • Wick products
  • magnetohydrodynamics system
  • regularity structures
  • renormalization
  • strong Feller

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