Alliot, Frédéric; Amrouche, Chérif Stokes problem in \(\mathbb{R}^n\) and weighted Sobolev spaces. (Problème de Stokes dans \(\mathbb{R}^n\) et espaces de Sobolev avec poids.) (French. Abridged English version) Zbl 0894.35082 C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 12, 1247-1252 (1997). Summary: We present isomorphism results for the Stokes problem in \(\mathbb{R}^n\) using weighted Sobolev spaces and we study the asymptotic behaviour of the solutions. We also study this problem with data in the Hardy space \({\mathcal H}^1(\mathbb{R}^n)\) as well as a few properties of solenoidal functions. Cited in 3 Documents MSC: 35Q30 Navier-Stokes equations 35B40 Asymptotic behavior of solutions to PDEs 76D07 Stokes and related (Oseen, etc.) flows Keywords:isomorphism results; Stokes problem in \(\mathbb{R}^n\); weighted Sobolev spaces; solenoidal functions PDFBibTeX XMLCite \textit{F. Alliot} and \textit{C. Amrouche}, C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 12, 1247--1252 (1997; Zbl 0894.35082) Full Text: DOI