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.

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.

Modeling of the Vortex-Structure in a Particle-Laden Mixing-Layer

2005 ◽  
Author(s):  
Jens A. Melheim ◽  
Stefan Horender ◽  
Martin Sommerfeld
Keyword(s):  
Vortex Structure ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Mixing Layer ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Calculated Concentration ◽  
Langevin Model ◽  
Particle Velocities

Numerical calculations of a particle-laden turbulent horizontal mixing-layer based on the Eulerian-Lagrangian approach are presented. Emphasis is given to the determination of the stochastic fluctuating fluid velocity seen by the particles in anisotropic turbulence. The stochastic process for the fluctuating velocity is a “Particle Langevin equation Model”, based on the Simplified Langevin Model. The Reynolds averaged Navier-Stokes equations are closed by the standard k-epsilon turbulence model. The calculated concentration profile and the mean, the root-mean-square (rms) and the cross-correlation terms of the particle velocities are compared with particle image velocimetry (PIV) measurements. The numerical results agree reasonably well with the PIV data for all of the mentioned quantities. The importance of the modeled vortex structure “seen” by the particles is discussed.

scholarly journals Mathematical Model for the Electrokinetic Instability of Electrolyte Flow

2019 ◽  
Vol 224 ◽  
pp. 02003
Author(s):  
Andrey Shobukhov
Keyword(s):  
Electric Potential ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Steady State Solution ◽  
Stability Loss ◽  
Navier Stokes ◽  
Ion Distribution ◽  
Navier Stokes Equations ◽  
Dilute Aqueous Solution

We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.

Weak Morrey spaces and strong solutions to the Navier-Stokes equations

2007 ◽  
Vol 50 (10) ◽  
pp. 1401-1417 ◽  
Author(s):  
Chang-xing Miao ◽  
Bao-quan Yuan
Keyword(s):  
Stokes Equations ◽  
Strong Solutions ◽  
Morrey Spaces ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Weak Morrey Spaces
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