Global pathwise solutions of an abstract stochastic equation
Analysis of PDEs
2024-07-02 v1 Probability
Abstract
We establish the existence and uniqueness of the maximal pathwise solution for an abstract nonlinear stochastic evolutional equation, which takes the two and three dimensional stochastic Navier-Stokes equations as a typical model, forced by a multiplicative white noise, and show that the pathwise solution exists globally in time in a positive probability when the initial data is sufficiently small. Moreover, a global pathwise solution is obtained for the stochastic Navier-Stokes equations defined on torus when the data is properly regular and small.
Cite
@article{arxiv.2407.00722,
title = {Global pathwise solutions of an abstract stochastic equation},
author = {Y. -X. Lin and Y. -G. Wang},
journal= {arXiv preprint arXiv:2407.00722},
year = {2024}
}