Differential and Integral Equations

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

Hiroyuki Tsurumi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Permanent link to this document
https://projecteuclid.org/euclid.die/1554256869

Mathematical Reviews number (MathSciNet)
MR3938342

Zentralblatt MATH identifier
07070543

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 42B37: Harmonic analysis and PDE [See also 35-XX]

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


Export citation