ETD

• flow approach
• Navier Stokes
• singular SPDE
• subcritical regime

This thesis constructs solutions to the incompressible stochastic Navier–Stokes equations on the two-dimensional torus driven by fractional space-time white noise in the subcritical regime. We implement Paweł Duch’s flow equation approach, marking its first application to a fluid dynamics setting.

Renormalization is achieved via space-independent counterterms that set macroscopic boundary conditions. By restricting the dynamics to a sufficiently small time interval $T$, we handle a fixed nonlinearity strength ($\lambda=1$) and prove the almost sure convergence of the regularized solutions to a unique limiting distribution in Besov spaces.