Addendum to the Paper “Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations″, Advanced Nonlinear Studies 6 (2006), 411-436

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Tomás Caraballo ◽  
José Real ◽  
Peter E. Kloeden
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Dimensional System ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equations ◽  
Three Dimensional System

AbstractIn this paper we improve Theorem 7 in [1] which deals with the existence and uniqueness of solutions of the three dimensional globally modified Navier-Stokes equations.

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.

scholarly journals THREE-DIMENSIONAL SYSTEM OF GLOBALLY MODIFIED NAVIER–STOKES EQUATIONS WITH DELAY

2010 ◽  
Vol 20 (09) ◽  
pp. 2869-2883 ◽  
Author(s):  
TOMÁS CARABALLO ◽  
JOSÉ REAL ◽  
ANTONIO M. MÁRQUEZ
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Pullback Attractor ◽  
Dimensional System ◽  
Navier Stokes Equations ◽  
Three Dimensional System ◽  
Equations With Delay

We prove the existence and uniqueness of strong solutions of a three-dimensional system of globally modified Navier–Stokes equations with delay in the locally Lipschitz case. The asymptotic behavior of solutions, and the existence of pullback attractor are also analyzed.

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)’.

scholarly journals On the existence and uniqueness of solutions to stochastic three-dimensional Lagrangian averaged Navier–Stokes equations

2005 ◽  
Vol 462 (2066) ◽  
pp. 459-479 ◽  
Author(s):  
Tomás Caraballo ◽  
José Real ◽  
Takeshi Taniguchi
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stochastic Version ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We prove the existence and uniqueness of solutions for a stochastic version of the three-dimensional Lagrangian averaged Navier–Stokes equation in a bounded domain. To this end, we previously prove some existence and uniqueness results for an abstract stochastic equation and justify that our model falls within this framework.

scholarly journals Three dimensional system of globally modified Navier-Stokes equations with infinite delays

2010 ◽  
Vol 14 (2) ◽  
pp. 655-673 ◽  
Author(s):  
Pedro Marín-Rubio ◽  
◽  
Antonio M. Márquez-Durán ◽  
José Real ◽  
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Dimensional System ◽  
Navier Stokes Equations ◽  
Infinite Delays ◽  
Three Dimensional System

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.

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