In this paper we study well-posedness of a second order SPDE with multiplicative noise on the torus $\mathbb{T} = [0,2\pi]$. The equation is considered in $L^p((0,T)\times\Omega;L^q(\mathbb{T}))$ for $p,q\in (1, \infty)$. It is well-known that if the noise is of gradient…