scholarly journals Very weak solutions and large uniqueness classes of stationary Navier–Stokes equations in bounded domains of R2

2006 ◽  
Vol 227 (2) ◽  
pp. 564-580 ◽  
Author(s):  
R. Farwig ◽  
G.P. Galdi ◽  
H. Sohr
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Very Weak Solutions ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

scholarly journals On the construction of suitable weak solutions to the 3D Navier–Stokes equations in a bounded domain by an artificial compressibility method

2017 ◽  
Vol 20 (01) ◽  
pp. 1650064 ◽  
Author(s):  
Luigi C. Berselli ◽  
Stefano Spirito
Keyword(s):  
Bounded Domain ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Suitable Weak Solutions ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method

We prove that suitable weak solutions of 3D Navier–Stokes equations in bounded domains can be constructed by a particular type of artificial compressibility approximation.

Weak Solutions of the Navier–Stokes Equations

2006 ◽  
Author(s):  
Jean-Yves Chemin ◽  
Benoit Desjardins ◽  
Isabelle Gallagher ◽  
Emmanuel Grenier
Keyword(s):  
Unbounded Domain ◽  
Mathematical Analysis ◽  
Weak Solutions ◽  
Spectral Properties ◽  
Stokes Equations ◽  
Stokes Operator ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Navier Stokes Equations ◽  
Compactness Result

The mathematical analysis of the incompressible Stokes and Navier–Stokes equations in a possibly unbounded domain Ω of Rd (d = 2 or 3) is the purpose of this chapter. Notice that no regularity assumptions will be required on the domain Ω. Because of the compactness result stated in Theorem 1.3, page 27, the case of bounded domains will be different (in fact slightly simpler) than the case of general domains. The study of the spectral properties of the Stokes operator previously defined relies on the study of its inverse, which is in fact much easier. We shall restrict ourselves here to the case of the homogeneous Stokes operator which is adapted to the case of a bounded domain.

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