Initial-boundary value problem for stochastic transport equations

This paper concerns the Dirichlet initial-boundary value problem for stochastic transport equations with non-regular coefficients. First, the existence and uniqueness of the strong stochastic traces is proved. The existence of weak solutions relies on the strong stochastic traces, and also on the pa...

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Veröffentlicht in:	Stochastic partial differential equations : analysis and computations 2021-09, Vol.9 (3), p.674-701, Article 674
Hauptverfasser:	Neves, Wladimir, Olivera, Christian
Format:	Artikel
Sprache:	eng
Schlagworte:	Boundary value problems Computational Mathematics and Numerical Analysis Computational Science and Engineering Dirichlet problem Divergence Fields (mathematics) Mathematical analysis Mathematics Mathematics and Statistics Numerical Analysis Partial Differential Equations Probability Theory and Stochastic Processes Statistical Theory and Methods Transport equations Uniqueness
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Beschreibung
Zusammenfassung:	This paper concerns the Dirichlet initial-boundary value problem for stochastic transport equations with non-regular coefficients. First, the existence and uniqueness of the strong stochastic traces is proved. The existence of weak solutions relies on the strong stochastic traces, and also on the passage from the Stratonovich into Itô’s formulation for bounded domains. Moreover, the uniqueness is established without the divergence of the drift vector field bounded from below.
ISSN:	2194-0401 2194-041X
DOI:	10.1007/s40072-020-00180-9