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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Article dans une revue
Journal of Functional Analysis, Elsevier, 2013, 264, pp.1329-1354. <10.1016/j.jfa.2013.01.003>
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https://hal.archives-ouvertes.fr/hal-01017915
Contributeur : Ennio Fedrizzi <>
Soumis le : jeudi 3 juillet 2014 - 13:17:02
Dernière modification le : jeudi 27 avril 2017 - 09:46:12

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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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