scholarly journals Existence and uniqueness of global solutions for the modified anisotropic 3D Navier−Stokes equations

2016 ◽  
Vol 50 (6) ◽  
pp. 1817-1823 ◽  
Author(s):  
Hakima Bessaih ◽  
Saber Trabelsi ◽  
Hamdi Zorgati
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Global Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations

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.

scholarly journals The Navier–Stokes regularity problem

2020 ◽  
Vol 378 (2174) ◽  
pp. 20190526
Author(s):  
James C. Robinson
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Regularity Of Solutions ◽  
Navier Stokes ◽  
Initial Condition ◽  
Theme Issue ◽  
Uniqueness Of Solutions ◽  
Rigorous Results ◽  
Navier Stokes Equations

There is currently no proof guaranteeing that, given a smooth initial condition, the three-dimensional Navier–Stokes equations have a unique solution that exists for all positive times. This paper reviews the key rigorous results concerning the existence and uniqueness of solutions for this model. In particular, the link between the regularity of solutions and their uniqueness is highlighted. This article is part of the theme issue ‘Stokes at 200 (Part 1)’.

GENESIS OF A SOURCE/SINK LINE INTO A SINGULAR UPDRAFT

1998 ◽  
Vol 08 (03) ◽  
pp. 431-444 ◽  
Author(s):  
JOËL CHASKALOVIC
Keyword(s):  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Vortex Line ◽  
Stokes Equations ◽  
Local Existence ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Local Existence And Uniqueness ◽  
Source Sink

Mathematical models applied to tornadoes describe these kinds of flows as an axisymmetric fluid motion which is restricted for not developing a source or a sink near the vortex line. Here, we propose the genesis of a family of a source/sink line into a singular updraft which can modeled one of the step of the genesis of a tornado. This model consists of a three-parameter family of fluid motions, satisfying the steady and incompressible Navier–Stokes equations, which vanish at the ground. We establish the local existence and uniqueness for these fields, at the neighborhood of a nonrotating singular updraft.

Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations

2006 ◽  
Vol 6 (3) ◽  
Author(s):  
Tomás Caraballo ◽  
José Real ◽  
Peter E. Kloeden
Keyword(s):  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Dimensional System ◽  
Navier Stokes Equations ◽  
Three Dimensional System

AbstractWe prove the existence and uniqueness of strong solutions of a three dimensional system of globally modified Navier-Stokes equations. The flattening property is used to establish the existence of global V -attractors and a limiting argument is then used to obtain the existence of bounded entire weak solutions of the three dimensional Navier-Stokes equations with time independent forcing.

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