Algebra properties in Fourier-Besov spaces and their applications
type: Item
instance of: scholarly article
title: Algebra properties in Fourier-Besov spaces and their applications
zbMATH Open document ID: 1415.46026
DOI: 10.1155/2018/3629179
author: Xuhuan Zhou
author: Weiliang Xiao
published in: Journal of Function Spaces
publication date: 2019-03-21T00:00:00Z
review text: Summary: We estimate the norm of the product of two scale functions in Fourier-Besov spaces. As applications of these algebra properties, we establish the global well-posedness for small initial data and local well-posedness for large initial data of the generalized Navier-Stokes equations. Particularly, we give a blow-up criterion of the solutions in Fourier-Besov spaces as well as a space analyticity of Gevrey regularity.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 7040439
zbMATH Keywords: Fourier-Besov spaces
zbMATH Keywords: global well-posedness
zbMATH Keywords: small initial data
zbMATH Keywords: generalized Navier-Stokes equations
zbMATH Keywords: Gevrey regularity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/3629179
OpenAlex ID: W2903299040
cites work: On the Navier-Stokes initial value problem. I
cites work: Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
cites work: Q4223061
cites work: Well-posedness for the Navier-Stokes equations
cites work: Q4782579
cites work: Q5890172
cites work: Generalized MHD equations.
cites work: The generalized incompressible Navier-Stokes equations in Besov spaces
cites work: Lower bounds for an integral involving fractional Laplacians and the generalized Navier-Stokes equations in Besov spaces
cites work: Homothetic variant of fractional Sobolev space with application to Navier-Stokes system
cites work: Well-posedness and regularity of generalized Navier-Stokes equations in some critical \(Q\)-spaces
cites work: Generalized Navier-Stokes equations with initial data in local \(Q\)-type spaces
cites work: Well-posedness for fractional Navier-Stokes equations in critical spaces \(\dot B _{\infty, \infty}^{-(2\beta-1)}(\mathbb R^n)\)
cites work: Well-posedness for fractional Navier-Stokes equations in the largest critical spaces \(\dot B_{\infty ,\infty}^{ -(2\beta - 1)} (\mathbb R^n)\)
cites work: Ill-posedness for subcritical hyperdissipative Navier-Stokes equations in the largest critical spaces
cites work: Well-posedness and ill-posedness for the 3D generalized Navier-Stokes equations in \(\dot{F}^{-\alpha,r}_{\frac{3}{\alpha-1}}\)
cites work: Smooth or singular solutions to the Navier-Stokes system?
cites work: Global well-posedness for Keller-Segel system in Besov type spaces
cites work: Global well-posedness for Navier-Stokes equations in critical Fourier-Herz spaces
cites work: Mixed Morrey spaces and their applications to partial differential equations
cites work: Global mild solutions of Navier‐Stokes equations
cites work: On dispersive effect of the Coriolis force for the stationary Navier-Stokes equations
cites work: Estimates of the Sobolev norm of a product of two functions
cites work: Q4668619
cites work: Gevrey class regularity for the solutions of the Navier-Stokes equations
cites work: Editorial board
cites work: Space analyticity for the Navier-Stokes and related equations with initial data in \(L^p\)
cites work: Gevrey regularity for a class of dissipative equations with applications to decay
cites work: Existence and analyticity of Lei-Lin solution to the Navier-Stokes equations
cites work: Global well-posedness and long time decay of fractional Navier-Stokes equations in Fourier-Besov spaces
cites work: Commutators and generalized local Morrey spaces
Wikidata QID: Q128892564
description: scientific article; zbMATH DE number 7040439