Well-posedness for stochastic fractional navier-stokes equation in critical Fourier-Besov-Morrey spaces

Abstract

This work considers the 3-D stochastic fractional Navier-Stokes equation driven by multiplicative noise in critical Fourier-Besov-Morrey spaces \(\mathcal {F\dot{N}}_{p,h,r}^{1-2\beta +\frac{3}{p^{\prime }}+\frac{h}{p}}(\mathbb {R}^{3})\). We establish the local existence and uniqueness of the solutions to the concerned equation and we prove the global existence in the probabilistic sense when the initial data are small.