Weak Solutions for Compressible Navier–Stokes–Fourier System in Two Space Dimensions with Adiabatic Exponent Almost One

2021 ◽  
Vol 172 (1) ◽  
Author(s):  
Milan Pokorný ◽  
Emil Skříšovský
Keyword(s):  
Weak Solutions ◽  
Navier Stokes ◽  
Adiabatic Exponent ◽  
Two Space Dimensions

References and Remarks on the Navier–Stokes Equations

2006 ◽  
Author(s):  
Jean-Yves Chemin ◽  
Benoit Desjardins ◽  
Isabelle Gallagher ◽  
Emmanuel Grenier
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Seminal Paper ◽  
Global Existence Of Solutions ◽  
Regularity Properties ◽  
Whole Space ◽  
Two Space Dimensions ◽  
Fundamental Paper

The purpose of this chapter is to give some historical landmarks to the reader. The concept of weak solutions certainly has its origin in mechanics; the article by C. Oseen [100] is referred to in the seminal paper by J. Leray. In that famous article, J. Leray proved the global existence of solutions of (NSν) in the sense of Definition 2.5, page 42, in the case when Ω = R3. The case when Ω is a bounded domain was studied by E. Hopf in. The study of the regularity properties of those weak solutions has been the purpose of a number of works. Among them, we recommend to the reader the fundamental paper of L. Caffarelli, R. Kohn and L. Nirenberg. In two space dimensions, J.-L. Lions and G. Prodi proved in [91] the uniqueness of weak solutions (this corresponds to Theorem 3.2, page 56, of this book). Theorem 3.3, page 58, of this book shows that regularity and uniqueness are two closely related issues. In the case of the whole space R3, theorems of that type have been proved by J. Leray in.

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.

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