scholarly journals Local well-posedness of a dispersive Navier-Stokes system

2011 ◽  
Vol 60 (2) ◽  
pp. 517-576 ◽  
Author(s):  
C. David Levermore ◽  
Weiran Sun
Keyword(s):  
Stokes System ◽  
Navier Stokes ◽  
Well Posedness

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 Global well-posedness for a Boussinesq–Navier–Stokes system with critical dissipation

2010 ◽  
Vol 249 (9) ◽  
pp. 2147-2174 ◽  
Author(s):  
Taoufik Hmidi ◽  
Sahbi Keraani ◽  
Frédéric Rousset
Keyword(s):  
Stokes System ◽  
Navier Stokes ◽  
Well Posedness
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