Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞.

Asymptotic Stability for One-dimensional Motion of Non-Newtonian Compressible Fluids

Rarefaction wave solutions for a one-dimensional model system associated with nomNewtonian compressible fluid are investigated in terms of asymptotic stability. The rarefaction wave solution is proved to be asymptotically stable, provided the initial disturbance is suitably small. The proof is given by the elemental L2 energy method.

Unsteady Flow of Shear-Thinning non-Newtonian Incompressible Fluid Through a Twin-Screw Extruder

The unsteady flow of viscous incompressible shear-thinning non-Newtonian fluid with mixed bound- ary is investigated. The boundary condition on the outflow is the modified natural boundary condition, it con- tains the additional nonlinear term, which enables us to control the kinetic energy of the backward flow. The global existence of weak solution is proved. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.

Asymptotic Stability of Periodic Solution for Compressible Viscous van der Waals Fluids

This paper is concerned with the asymptotic stability of the periodic solution to a one-dimensional model system for the compressible viscous van der Waals fluid in Eulerian coordinates. If the initial density and initial momentum are suitably close to the average density and average momentum, then the solution is proved to tend toward a stationary solution as t -→∞.

Navier-Stokes/Allen-Cahn System with Generalized Navier Boundary Condition

In this paper,we focus on the immiscible compressible two-phase flow described by the coupled compressible Navier-Stokes system and the modified Allen-Cahn equations.The generalized Navier boundary condition and the relaxation boundary condition are established in order to solve the problem of moving contact lines on the solid boundary by using the principle of minimum energy dissipation.The existence and uniqueness for local strong solution in three dimensional bounded domain for this type of boundary value problem is obtained by the elementary energy method and the maximum principle.

On the Motion of Shear-Thinning Heat-Conducting Incompressible Fluid-Rigid System

The full Navier-Stokes-Fourier system with mixed boundary condition that describes the motion of shear-thinning and incompressible viscous fluid in a rotating multi-screw extruder is investigated. The viscosity is assumed to depend on the shear rate and the temperature. The global existence of suitable weak solutions is established. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.

Partial Regularity of Suitable Weak Solutions to the System of the Incompressible Shear-thinning Flow

This paper is devoted to the partial regularity of suitable weak solutions to the system of the incompressible shear-thinning flow in a bounded domainΩ■R^(n),n≥2.It is proved that there exists a suitable weak solution of the shear-thinning fluid in the n-D smooth bounded domain(for n≥2).For 3 D model,it is proved that the singular points are concentrated on a closed set whose 1 dimensional Hausdorff measure is zero.