A note on \(W^{\gamma}_p\)-theory of linear stochastic parabolic partial differential systems (Q1761485)

The aim of the paper is to construct an \(L^p\)-theory for the general stochastic parabolic system \[ du^k= (a^{ij}_{kr}u^r_{x^ix^j} + b^i_{kr}u^r_{x^i} +c_{kr}u^r + f^k)dt + (\sigma^i_{kr,m}u^r_{x^i} +\nu_{kr,m}u^r + g^k_m)dw^m_{t} \] on \(t> 0\) and \(x\in \mathbb R^d\) with the initial conditions \(u^k(0)= u^k_0\). This system models the interactions between diffusive quantities under physical phenomena like convection. The \(L^2\)-theory for the systems of this type exists. The authors construct an \(L^p\)-theory by adopting the strategy according to which the theory of stochastic partial differential equations is constructed.