caa a22 4500 606194274 CHVBK 20210128100913.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00030-015-0321-6 doi (NATIONALLICENCE)springer-10.1007/s00030-015-0321-6 Wellposedness for stochastic continuity equations with Ladyzhenskaya-Prodi-Serrin condition [Elektronische Daten] [Wladimir Neves, Christian Olivera] 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. Springer Basel, 2015 Stochastic partial differential equation nationallicence Continuity equation nationallicence Well-posedness nationallicence Stochastic characteristic method nationallicence Cauchy problem nationallicence Neves Wladimir Departamento de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária, C.P. 68530, 21945-970, Rio de Janeiro, Brazil aut Olivera Christian Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970, Campinas, SP, Brazil aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1247-1258 1021-9722 22:5<1247 2015 22 30 https://doi.org/10.1007/s00030-015-0321-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0321-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Neves Wladimir Departamento de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária, C.P. 68530, 21945-970, Rio de Janeiro, Brazil aut NATIONALLICENCE 700 1- Olivera Christian Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970, Campinas, SP, Brazil aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1247-1258 1021-9722 22:5<1247 2015 22 30