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- W4300107894 abstract "The present article is devoted to well-posedness by noise for the continuity equation. Namely, we consider the continuity equation with non-linear and partially degenerate stochastic perturbations in divergence form. We prove the existence and uniqueness of entropy solutions under hypotheses on the velocity field which are weaker than those required in the deterministic setting. This extends related results of [Flandoli, Gubinelli, Priola; Invent. Math., 2010] applicable for linear multiplicative noise to a non-linear setting. The existence proof relies on a duality argument which makes use of the regularity theory for fully non-linear parabolic equations." @default.
- W4300107894 created "2022-10-03" @default.
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- W4300107894 date "2017-10-13" @default.
- W4300107894 modified "2023-09-27" @default.
- W4300107894 title "Stochastic continuity equations with conservative noise" @default.
- W4300107894 doi "https://doi.org/10.48550/arxiv.1710.04906" @default.
- W4300107894 hasPublicationYear "2017" @default.
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