Wellposedness for stochastic continuity equations with Ladyzhenskaya–Prodi–Serrin condition

We consider the stochastic divergence-free continuity equations with Ladyzhenskaya–Prodi–Serrin condition. Wellposedness is proved meanwhile uniqueness may fail for the deterministic PDE. The main issue of strong uniqueness, in the probabilistic sense, relies on stochastic characteristic method and...

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Bibliographic Details
Published in:Nonlinear differential equations and applications 2015-10, Vol.22 (5), p.1247-1258
Main Authors: Neves, Wladimir, Olivera, Christian
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:We consider the stochastic divergence-free continuity equations with Ladyzhenskaya–Prodi–Serrin condition. Wellposedness is proved meanwhile uniqueness may fail for the deterministic PDE. The main issue of strong uniqueness, in the probabilistic sense, relies on stochastic characteristic method and the generalized Itô–Wentzell–Kunita formula. The stability property for the unique solution is proved with respect to the initial data. Moreover, a persistence result is established by a representation formula.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-015-0321-6