## Differential and Integral Equations

### The stationary Navier-Stokes equations in the scaling invariant Triebel-Lizorkin spaces

Hiroyuki Tsurumi

#### Abstract

We consider the stationary Navier-Stokes equations in $\mathbb{R}^n$ for $n\ge 3$. We show the existence and uniqueness of solutions in the homogeneous Triebel-Lizorkin space $\dot F^{-1+\frac{n}{p}}_{p,q}$ with $1 < p\leq n$ for small external forces in $\dot F^{-3+\frac{n}{p}}_{p,q}$. Our method is based on the boundedness of the Riesz transform, the para-product formula, and the embedding theorem in homogeneous Triebel-Lizorkin spaces. Moreover, it is proved that under some additional assumption on external forces, our solutions actually have more regularity.

#### Article information

Source
Differential Integral Equations, Volume 32, Number 5/6 (2019), 323-336.

Dates
First available in Project Euclid: 3 April 2019

https://projecteuclid.org/euclid.die/1554256869

Mathematical Reviews number (MathSciNet)
MR3938342

Zentralblatt MATH identifier
07070543

#### Citation

Tsurumi, Hiroyuki. The stationary Navier-Stokes equations in the scaling invariant Triebel-Lizorkin spaces. Differential Integral Equations 32 (2019), no. 5/6, 323--336. https://projecteuclid.org/euclid.die/1554256869