Existence and Uniqueness of Solutions to Heat Equations with Hysteresis Coupled with Navier–Stokes Equations in 2D and 3D

2015 ◽  
Vol 17 (3) ◽  
pp. 577-597
Author(s):  
Yutaka Tsuzuki
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Heat Equations ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equations ◽  
2D And 3D

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)’.

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.

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.

scholarly journals Well-posedness of evolutionary Navier-Stokes equations with forces of low regularity on two-dimensional domains

2021 ◽  
Author(s):  
Karl Kunisch ◽  
Eduardo Renteria Casas
Keyword(s):  
Stokes Equation ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Well Posedness ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Arbitrary Dimensions ◽  
Parameter Ranges

Existence and uniqueness of solutions to the Navier-Stokes equation in dimension two with forces in the space $L^q( (0,T); \bWmop)$ for $p$ and $q$ in  appropriate parameter ranges are proven. The case of spatially measured-valued inhomogeneities is included. For the associated Stokes equation the well-posedness results are verified in arbitrary dimensions with $1 < p, q < \infty$ arbitrary.

ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS TO 2D G-BÉNARD PROBLEM IN UNBOUNDED DOMAINS

2020 ◽  
Vol 65 (6) ◽  
pp. 23-30
Author(s):  
Thinh Tran Quang ◽  
Thuy Le Thi
Keyword(s):  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Stokes Equations ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equations ◽  
Bénard Problem ◽  
Benard Problem ◽  
Homogeneous Dirichlet Boundary Conditions

We consider the 2D g-Bénard problem in domains satisfying the Poincaré inequality with homogeneous Dirichlet boundary conditions. We prove the existence and uniqueness of global weak solutions. The obtained results particularly extend previous results for 2D g-Navier-Stokes equations and 2D Bénard problem.

scholarly journals Asymptotic Behavior of the Solutions of the Generalized Globally Modified Navier–Stokes Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Yonghong Duan ◽  
Xiaojuan Chai
Keyword(s):  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Global Attractors ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equations

The paper is concerned with the existence and the asymptotic behavior of solutions to a class of generalized Navier–Stokes equations, which generalises the so-called globally modified Navier–Stokes equations. The existence and uniqueness of solutions are proved under different assumptions on the dissipation and modification factors. For the asymptotic behavior of solutions, we prove the existence of global attractors in proper spaces. The results generalize some results derived in our previous work Ann. Polon. Math. 122(2):101–128(2019).

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