Martingale and weak solutions for a stochastic nonlocal Burgers equation on finite intervals

This work is about the existence of martingale solutions and weak solutions for a stochastic nonlocal Burgers equation on a one dimensional bounded domain. The existence of a martingale solution is shown by using a Galerkin approximation, Prokhorov's theorem and Skorokhod's embedding theorem. The same Galerkin approximation also leads to the existence of weak solution for the corresponding deterministic nonlocal Burgers equation on a bounded domain.