Global Strong Well-Posedness of the stochastic bidomain equations with FitzHugh-Nagumo transport

Abstract

Consider the bidomain equations from electrophysiology with FitzHugh--Nagumo transport subject to current noise, i.e., subject to stochastic forcing modeled by a cylindrical Wiener process. It is shown that this set of equations admits a unique global, strong pathwise solution within the setting of critical spaces. The proof is based on combining methods from stochastic and deterministic maximal regularity. In addition, the method of extrapolation spaces from deterministic evolution equations is transferred to the stochastic setting.