Existence of Strong Solutions for a System Coupling the Navier–Stokes Equations and a Damped Wave Equation

2012 ◽  
Vol 15 (2) ◽  
pp. 249-271 ◽  
Author(s):  
Julien Lequeurre
Keyword(s):  
Wave Equation ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Damped Wave Equation ◽  
Navier Stokes Equations ◽  
System Coupling

scholarly journals Local Existence of Strong Solutions of a Fluid–Structure Interaction Model

2020 ◽  
Vol 22 (4) ◽  
Author(s):  
Sourav Mitra
Keyword(s):  
Stokes Equations ◽  
Local Existence ◽  
Interaction Model ◽  
Strong Solutions ◽  
Coupled System ◽  
Elastic Structure ◽  
Navier Stokes ◽  
Beam Equation ◽  
Navier Stokes Equations ◽  
System Coupling

AbstractWe are interested in studying a system coupling the compressible Navier–Stokes equations with an elastic structure located at the boundary of the fluid domain. Initially the fluid domain is rectangular and the beam is located on the upper side of the rectangle. The elastic structure is modeled by an Euler–Bernoulli damped beam equation. We prove the local in time existence of strong solutions for that coupled system.

scholarly journals Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xiaoyuan Wang ◽  
Sirui Li ◽  
Tingting Wang
Keyword(s):  
Energy Estimate ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Strong Solutions ◽  
Approximate Solutions ◽  
Dynamical Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Tensor Parameter ◽  
System Coupling

AbstractWe consider the inertial Qian–Sheng’s Q-tensor dynamical model for the nematic liquid crystal flow, which can be viewed as a system coupling the hyperbolic-type equations for the Q-tensor parameter with the incompressible Navier–Stokes equations for the fluid velocity. We prove the existence and uniqueness of local in time strong solutions to the system with the initial data near uniaxial equilibrium. The proof is mainly based on the classical Friedrich method to construct approximate solutions and the closed energy estimate.

ON THE ASYMPTOTIC ANALYSIS OF THE BGK MODEL TOWARD THE INCOMPRESSIBLE LINEAR NAVIER–STOKES EQUATION

2010 ◽  
Vol 20 (08) ◽  
pp. 1299-1318 ◽  
Author(s):  
A. BELLOUQUID
Keyword(s):  
Asymptotic Analysis ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Uniqueness Theorems ◽  
Bgk Model ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stokes Systems ◽  
Global Strong Solutions

This paper deals with the analysis of the asymptotic limit for BGK model to the linearized Navier–Stokes equations when the Knudsen number ε tends to zero. The uniform (in ε) existence of global strong solutions and uniqueness theorems are proved for regular initial fluctuations. As ε tends to zero, the solution of BGK model converges strongly to the solution of the linearized Navier–Stokes systems. The validity of the BGK model is critically analyzed.

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