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May/June 2019 The stationary Navier-Stokes equations in the scaling invariant Triebel-Lizorkin spaces
Hiroyuki Tsurumi
Differential Integral Equations 32(5/6): 323-336 (May/June 2019).

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.

Citation

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Hiroyuki Tsurumi. "The stationary Navier-Stokes equations in the scaling invariant Triebel-Lizorkin spaces." Differential Integral Equations 32 (5/6) 323 - 336, May/June 2019.

Information

Published: May/June 2019
First available in Project Euclid: 3 April 2019

zbMATH: 07070543
MathSciNet: MR3938342

Subjects:
Primary: 35Q30, 42B37

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.32 • No. 5/6 • May/June 2019
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