scholarly journals Global Well-Posedness to the 3D Cauchy Problem of Nonhomogeneous Heat Conducting Navier–Stokes Equations with Vacuum and Large Oscillations

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Xin Zhong
Keyword(s):  
Cauchy Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Well Posedness ◽  
Navier Stokes Equations ◽  
Nonhomogeneous Heat

scholarly journals Global Well-Posedness for Fractional Navier-Stokes Equations in critical Fourier-Besov-Morrey Spaces

2017 ◽  
Vol 3 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Azzeddine El Baraka ◽  
Mohamed Toumlilin
Keyword(s):  
Cauchy Problem ◽  
Stokes Equations ◽  
Morrey Spaces ◽  
Navier Stokes ◽  
Well Posedness ◽  
Navier Stokes Equations ◽  
Small Initial Data ◽  
Localization Method ◽  
Fourier Localization ◽  
The Cauchy Problem

Abstract In this paper we study the Cauchy problem of the Fractional Navier-Stokes equations in critical Fourier-Besov-Morrey spaces FṄsp, λ,q(ℝ3) with . By making use of the Fourier localization method and the Littlewood-Paley theory as in [6] and [21], we get global well-posedness result with small initial data belonging to . The space FṄsp,λ,q(ℝ3) covers the classical spaces Ḃsq and FḂsp,q(ℝ3) (cf [7],[3], [19], [22]...). The result of this paper extends the works of [6] and [21].

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