Regular solutions of the stationary Navier-Stokes equations on high dimensional Euclidean space

Abstract

We study the existence of regular solutions of the incompressible stationary Navier-Stokes equations in $n$-dimensional Euclidean space with a given bounded external force of compact support. In dimensions $n\le 5$, the existence of such solutions was known. In this paper, we extend it to dimensions $n\le 15$.Comment: Exposition improved. To appear in Comm. Math. Phy