Artículos de revistas
Wellposedness For Stochastic Continuity Equations With Ladyzhenskaya–prodi–serrin Condition
Registro en:
Nonlinear Differential Equations And Applications. Birkhauser Verlag Ag, v. 22, n. 5, p. 1247 - 1258, 2015.
10219722
10.1007/s00030-015-0321-6
2-s2.0-84942305768
Institución
Resumen
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) 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. © 2015, Springer Basel. 22 5 1247 1258 2012/18739-0, FAPESP, Conselho Nacional de Desenvolvimento Científico e Tecnológico 2012/18780-0, FAPESP, Conselho Nacional de Desenvolvimento Científico e Tecnológico 2013/15795-9, FAPESP, Conselho Nacional de Desenvolvimento Científico e Tecnológico 308652/2013-4, CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico 460713/2014-0, CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico 484529/2013-7, CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Alberti, G., Bianchini, S., Crippa, G., Divergence-free vector fields in R (2010) J. 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