Global well-posedness of the incompressible fractional Navier–Stokes equations in Fourier–Besov spaces with variable exponents

2019 ◽  
Vol 77 (4) ◽  
pp. 1082-1090 ◽  
Author(s):  
Shaolei Ru ◽  
Muhammad Zainul Abidin
Keyword(s):  
Besov Spaces ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Well Posedness ◽  
Variable Exponents ◽  
Navier Stokes Equations

scholarly journals Global Well-Posedness and Long Time Decay of Fractional Navier-Stokes Equations in Fourier-Besov Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Weiliang Xiao ◽  
Jiecheng Chen ◽  
Dashan Fan ◽  
Xuhuan Zhou
Keyword(s):  
Besov Spaces ◽  
Critical Case ◽  
Stokes Equations ◽  
Global Solutions ◽  
Navier Stokes ◽  
Well Posedness ◽  
Time Decay ◽  
Navier Stokes Equations ◽  
The Cauchy Problem ◽  
Long Time

We study the Cauchy problem of the fractional Navier-Stokes equations in critical Fourier-Besov spacesFB˙p,q1-2β+3/p′. Some properties of Fourier-Besov spaces have been discussed, and we prove a general global well-posedness result which covers some recent works in classical Navier-Stokes equations. Particularly, our result is suitable for the critical caseβ=1/2. Moreover, we prove the long time decay of the global solutions in Fourier-Besov spaces.

scholarly journals Algebra Properties in Fourier-Besov Spaces and Their Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Xuhuan Zhou ◽  
Weiliang Xiao
Keyword(s):  
Initial Data ◽  
Besov Spaces ◽  
Blow Up ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Well Posedness ◽  
Gevrey Regularity ◽  
Navier Stokes Equations ◽  
Small Initial Data ◽  
Scale Functions

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.

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