Differential and Integral Equations

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

Hiroyuki Tsurumi

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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

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

First available in Project Euclid: 3 April 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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