Stochastic evolution equations with rough boundary noise

Abstract: We investigate the pathwise well-posedness of stochastic evolution equations perturbed by multiplicative Neumann boundary noise, such as fractional Brownian motion for $H\in(1/3,1/2]$. Combining the controlled rough path approach with the theory of extrapolation operators, we establish global existence of solutions and flows for such equations. For Dirichlet boundary noise we obtain similar results in the Young regime.