On global regular solutions to the Navier–Stokes equations with heat convection

2013 ◽  
Vol 108 (2) ◽  
pp. 155-184
Author(s):  
Piotr Kacprzyk
Keyword(s):  
Stokes Equations ◽  
Heat Convection ◽  
Navier Stokes ◽  
Regular Solutions ◽  
Navier Stokes Equations

scholarly journals Sobolev regular solutions for the incompressible Navier–Stokes equations in higher dimensions: asymptotics and representation formulae

2020 ◽  
Author(s):  
Weiping Yan ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Asymptotic Expansion ◽  
Stokes Equations ◽  
Higher Dimensions ◽  
Finite Energy ◽  
Explicit Representation ◽  
Navier Stokes ◽  
Regular Solutions ◽  
Smooth Bounded Domain ◽  
Navier Stokes Equations ◽  
Expansion Formulae

Abstract In this paper, we consider the steady incompressible Navier–Stokes equations in a smooth bounded domain $$\Omega \subset \mathbb R^n$$ Ω ⊂ R n with the dimension $$n\ge 3$$ n ≥ 3 . We first establish asymptotic expansion formulae of Sobolev regular finite energy solutions in $$\Omega$$ Ω . In the second part of this paper, explicit representation formulae of Sobolev regular solutions are showed in the regular polyhedron $$\Omega :=[0,T]^n$$ Ω : = [ 0 , T ] n .

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