scholarly journals Dispersive Effect of the Coriolis Force and the Local Well-Posedness for the Navier-Stokes Equations in the Rotational Framework

2015 ◽  
Vol 58 (3) ◽  
pp. 365-385 ◽  
Author(s):  
Tsukasa Iwabuchi ◽  
Ryo Takada
Keyword(s):  
Coriolis Force ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Well Posedness ◽  
Navier Stokes Equations ◽  
Dispersive Effect

scholarly journals Solutions of Navier-Stokes Equations with Coriolis Force in the Rotational Framework

2021 ◽  
Vol 31 (5) ◽  
pp. 54-57
Keyword(s):  
Coriolis Force ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mixed Norm ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equations ◽  
Interpolation Inequalities ◽  
Stokes Problems ◽  
Point Argument

In this article, for 0 ≤m<∞ and the index vectors q=(q_1,q_2 ,q_3 ),r=(r_1,r_2,r_3) where 1≤q_i≤∞,1<r_i<∞ and 1≤i≤3, we study new results of Navier-Stokes equations with Coriolis force in the rotational framework in mixed-norm Sobolev-Lorentz spaces H ̇^(m,r,q) (R^3), which are more general than the classical Sobolev spaces. We prove the existence and uniqueness of solutions to the Navier-Stokes equations (NSE) under Coriolis force in the spaces L^∞([0, T]; H ̇^(m,r,q) ) by using topological arguments, the fixed point argument and interpolation inequalities. We have achieved new results compared to previous research in the Navier-Stokes problems.

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.

Sign in / Sign up

Export Citation Format

Share Document