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Noise Prevents Singularities in Linear Transport Equations

Abstract : A stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated. The drift is assumed only integrable to a certain power. Opposite to the deterministic case where smooth initial conditions may develop discontinuities, we prove that a certain Sobolev degree of regularity is maintained, which implies Hölder continuity of solutions. The proof is based on a careful analysis of the associated stochastic flow of characteristics.
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https://hal.archives-ouvertes.fr/hal-01017915
Contributor : Ennio Fedrizzi <>
Submitted on : Thursday, July 3, 2014 - 1:17:02 PM
Last modification on : Friday, March 27, 2020 - 3:58:35 AM

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Ennio Fedrizzi, Franco Flandoli. Noise Prevents Singularities in Linear Transport Equations. Journal of Functional Analysis, Elsevier, 2013, 264, pp.1329-1354. ⟨10.1016/j.jfa.2013.01.003⟩. ⟨hal-01017915⟩

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