Moving least squares-based multi-functional sensing technique for estimating viscosity and density of ternary solution

In the osmotic dehydration process of food,on-line estimation of concentrations of two components in ternary solution with NaCl and sucrose was performed based on multi-functional sensing technique.Moving Least Squares were adopted in approximation procedure to estimate the viscosity of such interested ternary solution with the given data set.As a result,in one mode of using total experimental data as calibration data and validation data,the relative deviations of estimated viscosities are less than ±1.24%.In the other mode,by taking total experimental data except the ones for estimation as calibration data,the relative deviations are less than ±3.47%.In the same way,the density of ternary solution can be also estimated with deviations less than ± 0.11% and ± 0.30% respectively in these two models.The satisfactory and accurate results show the extraordinary efficiency of Moving Least Squares behaved in signal approximation for multi-functional sensors.

Global well-posedness of 3-D density-dependent Navier-Stokes system with variable viscosity

Given initial data(ρ0, u0) satisfying 0 < m ρ0≤ M, ρ0- 1 ∈ L2∩˙W1,r(R3) and u0 ∈˙H-2δ∩ H1(R3) for δ∈ ]1/4, 1/2[ and r ∈ ]6, 3/1- 2δ[, we prove that: there exists a small positive constant ε1,which depends on the norm of the initial data, so that the 3-D incompressible inhomogeneous Navier-Stokes system with variable viscosity has a unique global strong solution(ρ, u) whenever‖ u0‖ L2 ‖▽u0 ‖L2 ≤ε1 and ‖μ(ρ0)- 1‖ L∞≤ε0 for some uniform small constant ε0. Furthermore, with smoother initial data and viscosity coefficient, we can prove the propagation of the regularities for such strong solution.

Global well-posedness for the dynamical Q-tensor model of liquid crystals

We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.