Well-posedness of the vector advection equations by stochastic perturbation

A linear stochastic vector advection equation is considered. The equation may model a passive magnetic field in a random fluid. The driving velocity field is a integrable to a certain power, and the noise is infinite dimensional. We prove that, thanks to the noise, the equation is well posed in a su...

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Bibliographic Details
Published in:Journal of evolution equations 2018-06, Vol.18 (2), p.277-301
Main Authors: Flandoli, Franco, Olivera, Christian
Format: Article
Language:English
Subjects:
Advection
Analysis
Mathematics
Mathematics and Statistics
Noise
Velocity distribution
Well posed problems
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Summary:A linear stochastic vector advection equation is considered. The equation may model a passive magnetic field in a random fluid. The driving velocity field is a integrable to a certain power, and the noise is infinite dimensional. We prove that, thanks to the noise, the equation is well posed in a suitable sense, opposite to what may happen without noise.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-017-0401-7