scholarly journals Existence and uniqueness of steady weak solutions to the Navier–Stokes equations in $\mathbb {R}^{2}$

2018 ◽  
Vol 146 (10) ◽  
pp. 4429-4445 ◽  
Author(s):  
Julien Guillod ◽  
Peter Wittwer
Keyword(s):  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
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 Weak solutions to the time-fractional g-Navier–Stokes equations and optimal control

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sultana Ben Aadi ◽  
Khalid Akhlil ◽  
Khadija Aayadi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Fractional Derivative ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Fractional Derivative

Abstract In this paper, we introduce the g-Navier–Stokes equations with time-fractional derivative of order α ∈ ( 0 , 1 ) {\alpha\in(0,1)} in domains of ℝ 2 {\mathbb{R}^{2}} . We then study the existence and uniqueness of weak solutions by means of the Galerkin approximation. Finally, an optimal control problem is considered and solved.

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