37 research outputs found
Wellposedness for stochastic continuity equations with Ladyzhenskaya-Prodi-Serrin condition
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 uniqueness
realies on stochastic characteristic method and the generalized
Ito-Ventzel-Kunita formula. Moreover, we prove a stability property for the
solution with respect to the initial datum.Comment: To appears in Nonlinear Differential Equations and Applications NoDE