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Stochastic Partial Differential Equations on Evolving Surfaces and Evolving Riemannian Manifolds

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arxiv 1208.5958 v1 pith:BC7M4V5Q submitted 2012-08-29 math.AP math.DG

C. M. Elliott , M. Hairer , M. R. Scott This is my paper · ORCID
classification math.APmath.DG
keywords differentialequationsmanifoldspartialriemannianstochasticevolvingsurfaces
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We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting of the analysis to stochastic partial differential equations. Considering mainly linear stochastic partial differential equations, we establish various existence and uniqueness theorems.

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  1. Lagrangian averaged stochastic advection by Lie transport for fluids

    math-ph 2019-08 conditional novelty 5.0 of 10

    The paper formulates LA SALT stochastic fluid equations whose mean field satisfies a closed Lie-Laplacian Navier-Stokes equation, and establishes well-posedness and fluctuation variance dynamics.

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