Global martingale solution for the stochastic Boussinesq system with zero dissipation

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Abstract

ABSTRACT: We study the two-dimensional stochastic Boussinesq system with zero dissipation and multiplicative noise. We show the existence of a martingale solution by a priori estimates using stochastic calculus, and applications of Prokhorov's, Skorokhod's, and martingale representation theorems. Due to the lack of dissipation, the proof requires higher regularity estimates, taking advantage of the structure of the nonlinear term. Moreover, we obtain the existence of the pressure term via an application of de Rham's theorem for processes.

Original languageEnglish
Pages (from-to)404-426
Number of pages23
JournalStochastic Analysis and Applications
Volume34
Issue number3
DOIs
StatePublished - May 3 2016

Keywords

  • Boussinesq system
  • Navier–Stokes equations
  • Prokhorov's theorem
  • Skorokhod's theorem
  • martingale solution

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