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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Neves, Wladimir [1] ; Olivera, Christian [2]
Total Authors: 2
Affiliation:
[1] Univ Fed Rio de Janeiro, Dept Matemat, BR-68530 Rio De Janeiro - Brazil
[2] Univ Estadual Campinas, Dept Matemat, BR-13081970 Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS; v. 22, n. 5, p. 1247-1258, OCT 2015.
Web of Science Citations: 8
Abstract

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 It-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. (AU)

FAPESP's process: 13/15795-9 - Stochastic partial differential equations
Grantee:Christian Horacio Olivera
Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
FAPESP's process: 12/18739-0 - Generalized functions and stochastic equations
Grantee:Christian Horacio Olivera
Support Opportunities: Regular Research Grants
FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
Grantee:Marco Antônio Teixeira
Support Opportunities: Research Projects - Thematic Grants