The Stokes Problem

Abstract

This Chapter is devoted to the Stokes system of differential equations, that can be written as

$$ \left\{ {\begin{array}{*{20}c} {a_0 u - \nu \Delta u + \nabla p = f in \Omega \subset \mathbb{R}^d , d = 2,3} \\ {div u = 0 in \Omega } \\ {u = 0 on \partial \Omega , } \\ \end{array} } \right. $$

(9.1)

where a₀≥0 and ν>0 are given constants, f: Ω → ℝd is a given function, while u: Ω → ℝd and p: Ω → ℝ are the problem unknowns.