THE STOKES PROBLEM IN ℝn: AN APPROACH IN WEIGHTED SOBOLEV SPACES

Abstract

We prove some existence, uniqueness and regularity results for the solutions to the Stokes problem in ℝn, n≥2 in weighted Sobolev spaces [Formula: see text]. This framework enables us to characterise for which data the problem has solutions with prescribed decay or growth at infinity. Moreover, we obtain an explicit representation as well as an asymptotic expansion of the solution for non-smooth decaying data. We also establish the density of smooth solenoidal vector fields in the subspace of [Formula: see text] such that div v=0.