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

TL;DR

This paper extends the known existence of regular solutions to the stationary Navier-Stokes equations from dimensions up to 5 to dimensions up to 15 in high-dimensional Euclidean spaces, considering bounded external forces.

Contribution

It broadens the dimensional range for which regular solutions of the stationary Navier-Stokes equations are known to exist, from n ≤ 5 to n ≤ 15.

Findings

Existence of regular solutions established for n ≤ 15

Extension from previous results limited to n ≤ 5

Applicable to bounded external forces with compact support

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 $n\le 15$.