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Incompressible Euler equations with stochastic forcing: A geometric approach

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  • Maurelli, Mario
  • Modin, Klas
  • Schmeding, Alexander

Abstract

We consider a stochastic version of Euler equations using the infinite-dimensional geometric approach as pioneered by Ebin and Marsden (1970). For the Euler equations on a compact manifold (possibly with smooth boundary) we establish local existence and uniqueness of a strong solution in spaces of Sobolev mappings (of high enough regularity). Our approach combines techniques from stochastic analysis and infinite-dimensional geometry and provides a novel toolbox to establish local well-posedness of stochastic non-linear partial differential equations.

Suggested Citation

  • Maurelli, Mario & Modin, Klas & Schmeding, Alexander, 2023. "Incompressible Euler equations with stochastic forcing: A geometric approach," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 101-148.
    • Handle: RePEc:eee:spapps:v:159:y:2023:i:c:p:101-148
    DOI: 10.1016/j.spa.2023.01.011
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    References listed on IDEAS

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    1. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
    2. Cruzeiro, Ana Bela & Shamarova, Evelina, 2009. "Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4034-4060, December.
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