scholarly journals Global Well-Posedness of Incompressible Elastodynamics in Three-Dimensional Thin Domain

2021 ◽  
Vol 53 (6) ◽  
pp. 6654-6696
Author(s):  
Yuan Cai ◽  
Fan Wang
Keyword(s):  
Three Dimensional ◽  
Well Posedness ◽  
Thin Domain

scholarly journals Analysis for Flow of an Incompressible Brinkman-Type Fluid in Thin Medium with Friction

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Soumia Manaa ◽  
Salah Boulaaras ◽  
Hamid Benseridi ◽  
Mourad Dilmi ◽  
Sultan Alodhaibi
Keyword(s):  
Fluid Flow ◽  
Variational Formulation ◽  
Reynolds Equation ◽  
Three Dimensional ◽  
Stationary Regime ◽  
Limit Problem ◽  
Brinkman Equation ◽  
Asymptotic Convergence ◽  
Thin Domain ◽  
Uniqueness Of The Solution

In this paper, we consider the Brinkman equation in the three-dimensional thin domain ℚ ε ⊂ ℝ 3 . The purpose of this paper is to evaluate the asymptotic convergence of a fluid flow in a stationary regime. Firstly, we expose the variational formulation of the posed problem. Then, we presented the problem in transpose form and prove different inequalities for the solution u ε , p ε independently of the parameter ε . Finally, these estimates allow us to have the limit problem and the Reynolds equation and establish the uniqueness of the solution.

Study of Stokes dynamical system in a thin domain with Fourier and Tresca boundary conditions

2019 ◽  
pp. 2150007 ◽  
Author(s):  
Y. Letoufa ◽  
H. Benseridi ◽  
M. Dilmi
Keyword(s):  
Boundary Conditions ◽  
Variational Formulation ◽  
Reynolds Equation ◽  
Mixed Boundary ◽  
Three Dimensional ◽  
Mixed Boundary Conditions ◽  
Dynamic Regime ◽  
Thin Domain ◽  
Problem Statement ◽  
Stokes Fluid

Asymptotic analysis of an incompressible Stokes fluid in a dynamic regime in a three-dimensional thin domain [Formula: see text] with mixed boundary conditions and Tresca friction law is studied in this paper. The problem statement and variational formulation of the problem are reformulated in a fixed domain. In which case, the estimates on velocity and pressure are proved. These estimates will be useful in order to give a specific Reynolds equation associated with variational inequalities and prove the uniqueness.

scholarly journals Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 218 ◽  
Author(s):  
Praveen Kalarickel Ramakrishnan ◽  
Mirco Raffetto
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Well Posedness ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
First Time

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

scholarly journals On well-posedness of a magnetization-variables model for Navier-Stokes equations with damping

2020 ◽  
Author(s):  
Abdelkerim Chaabani,
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Well Posedness ◽  
Energy Methods ◽  
Damping Term ◽  
Navier Stokes Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

This paper aims to establish existence and uniqueness results of weak and strong solution to the three-dimensional periodic magnetization-variables formulation to Navier-Stokes equations with damping term. Authors in precedent works addressed the question as to whether this model and similar ones without damping term possess a weak solution. In this vein, considering a damping term in the magnetization-variable formulation turned to be consequential as it enforces existence and uniqueness results. Energy methods, compactness methods are the main tools.

scholarly journals Global well-posedness for the three-dimensional incompressible viscous non-resistive MHD equations in an infinite slab

2021 ◽  
Author(s):  
Youyi Zhao
Keyword(s):  
Initial Data ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Well Posedness ◽  
Lagrangian Coordinates ◽  
Mathematical Approach ◽  
Compatibility Conditions ◽  
Finite Height ◽  
Infinite Slab ◽  
Mhd System

In this paper, we investigate the global well-posedness of the system of incompressible viscous non-resistive MHD fluids in a three-dimensional horizontally infinite slab with finite height. We reformulate our analysis to Lagrangian coordinates, and then develop a new mathematical approach to establish global well-posedness of the MHD system, which requires no nonlinear compatibility conditions on the initial data.

scholarly journals Well-Posedness of Strong Solutions to the Anelastic Equations of Stratified Viscous Flows

2020 ◽  
Vol 22 (3) ◽  
Author(s):  
Xin Liu ◽  
Edriss S. Titi
Keyword(s):  
Initial Data ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Viscous Flows ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Physical Vacuum ◽  
Well Posedness ◽  
Small Initial Data ◽  
Anelastic Equations

Abstract We establish the local and global well-posedness of strong solutions to the two- and three-dimensional anelastic equations of stratified viscous flows. In this model, the interaction of the density profile with the velocity field is taken into account, and the density background profile is permitted to have physical vacuum singularity. The existing time of the solutions is infinite in two dimensions, with general initial data, and in three dimensions with small initial data.

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