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.

GLOBAL CLASSICAL SOLUTIONS FOR A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL

2013 ◽  
Vol 10 (03) ◽  
pp. 537-562 ◽  
Author(s):  
MYEONGJU CHAE ◽  
KYUNGKEUN KANG ◽  
JIHOON LEE
Keyword(s):  
Stokes Equations ◽  
Particle Interaction ◽  
Three Dimensional ◽  
Interaction Model ◽  
Planck Equation ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Navier Stokes Equations ◽  
Global Classical Solutions ◽  
System Coupling

We consider a system coupling the compressible Navier–Stokes equations to the Vlasov–Fokker–Planck equation on three-dimensional torus. The coupling arises from a drag force exerted by each other. We establish the existence of the global classical solutions close to an equilibrium, and further prove that the solutions converge to the equilibrium exponentially fast.

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