Fundamental solutions for stationary Stokes systems with measurable coefficients

Abstract

We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space ${\mathbb{R}}^d$, $d\ge 3$, under the assumption that weak solutions of the system are locally Hölder continuous. We also discuss the existence and the pointwise bound of the Green function for the Stokes system with measurable coefficients on $\Omega$, where $\Omega$ is an unbounded domain such that the divergence equation is solvable. Such a domain includes, for example, half space and an exterior domain.

32 pages; accepted in Journal of Differential Equation

References in corpus (2)

• Global pointwise estimates for Green's matrix of second order elliptic systems
• Green's functions for elliptic and parabolic systems with Robin-type boundary conditions