On the Stokes problem with data in L 1

Abstract

We consider the steady Stokes equations in bounded and exterior domains Ω of $${{\mathbb{R}^3}}$$ with boundary data and forces in L 1. We prove existence and uniqueness of a weak solution with gradient in the Iwaniek–Sbordone grand Lebesgue space $${L^{\frac{3}{2})}}$$