Global well-posedness of strong solutions to the two-dimensional barotropic compressible Navier–Stokes equations with vacuum

2016 ◽  
Vol 67 (2) ◽  
Author(s):  
Li Fang ◽  
Zhenhua Guo
Keyword(s):  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Well Posedness ◽  
Two Dimensional ◽  
Navier Stokes Equations

Stability of Navier–Stokes Equations

2006 ◽  
Author(s):  
Jean-Yves Chemin ◽  
Benoit Desjardins ◽  
Isabelle Gallagher ◽  
Emmanuel Grenier
Keyword(s):  
Stokes System ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Well Posedness ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Three Space

In this chapter we intend to investigate the stability of the Leray solutions constructed in the previous chapter. It is useful to start by analyzing the linearized version of the Navier–Stokes equations, so the first section of the chapter is devoted to the proof of the well-posedness of the time-dependent Stokes system. The study will be applied in Section 3.2 to the two-dimensional Navier–Stokes equations, and the more delicate case of three space dimensions will be dealt with in Sections 3.3–3.5.

scholarly journals Well-posedness analysis of multicomponent incompressible flow models

2021 ◽  
Author(s):  
Dieter Bothe ◽  
Pierre-Etienne Druet
Keyword(s):  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Well Posedness ◽  
Navier Stokes Equations ◽  
Flow Models ◽  
Change Of Variables ◽  
Algebraic Formula ◽  
Time Existence ◽  
Specific Volumes

AbstractIn this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence of average volume on pressure, and a weighted sum of the partial mass densities stays constant. In this type of models, the velocity field in the Navier–Stokes equations is not solenoidal and, due to different specific volumes of the species, the pressure remains connected to the densities by algebraic formula. By means of a change of variables in the transport problem, we equivalently reformulate the PDE system as to eliminate positivity and incompressibility constraints affecting the density, and prove two type of results: the local-in-time well-posedness in classes of strong solutions, and the global-in-time existence of solutions for initial data sufficiently close to a smooth equilibrium solution.

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