Y spaces and global smooth solution of fractional Navier-Stokes equations with initial value in the critical oscillation spaces
type: Item
instance of: scholarly article
title: Y spaces and global smooth solution of fractional Navier-Stokes equations with initial value in the critical oscillation spaces
zbMATH Open document ID: 1394.35334
author: Qixiang Yang
author: Haibo Yang
published in: Journal of Differential Equations
publication date: 2018-02-06T00:00:00Z
review text: The Cauchy problem to the fractional Navier-Stokes equations is studied in the paper. \[ \frac{\partial u}{\partial t}+(u\cdot\nabla)u+(-\Delta)^\beta u-\nabla p=0,\quad \text{div}\,u=0, \quad x\in\mathbb{R}^n,\;t>0, \] \[ u(x,0)=u_0(x),\;x\in\mathbb{R}^n. \] Here \(n\geq 2\), \(1/2<\beta<1\), \((-\Delta)^\beta\) is the \(\beta\)-order Laplace operator. The problem is investigated in a wide class of spaces including Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces. It is proved that if the initial data \(u_0\) has a small norm then the problem has a unique smooth global solution. The spaces used are described in detail in the article. It should be noted that not all designations are defined, and this makes it difficult to read the work.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6834794
zbMATH Keywords: fractional Navier-Stokes equations
zbMATH Keywords: parameter Meyer wavelets
zbMATH Keywords: Besov-Morrey spaces
zbMATH Keywords: Triebel-Lizorkin-Morrey spaces
zbMATH Keywords: global solvability
reviewed by: Il'ya Sh. Mogilevskii
MaRDI profile type: Publication
full work available at URL: j.jde.2017.12.017
OpenAlex ID: W2781682182
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DOI: 10.1016/J.JDE.2017.12.017
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description: scientific article; zbMATH DE number 6834794