THE EXISTENCE AND DECAY ESTIMATES OF THE SOLUTIONS TO 3D STOCHASTIC NAVIER-STOKES EQUATIONS WITH ADDITIVE NOISE IN AN EXTERIOR DOMAIN

摘要

In this paper we consider the local existence and global existence with probability 1 - σ (0 ＜ σ ＜ 1) of pathwise solutions to the three-dimensional stochastic Navier-Stokes equation perturbed by a cylindrical Wiener processe W(t) in an exteriour domain: dX(t) = [-AX(t) + B (X(t)) + f_*(t)]dt + Φ(t)dW(t), where A = -PΔ is the Stokes operator, and f_*(t) and Φ(t) satisfy some conditions. We also consider the decay of pathwise solutions.