Stability of stochastic 2D Navier-Stokes equations with memory and Poisson jumps

The objective of this paper is to study the stability of the weak solutions of stochastic 2D Navier-Stokes equations with memory and Poisson jumps. The asymptotic stability of the stochastic Navier-Stoke equation as a semilinear stochastic evolution equation in Hilbert spaces is obtained in both mean square and almost sure senses. Our results can extend and improve some existing ones.

Computational Analysis of Effective Microfluidic Mixing Utilizing Surface Heterogeneity Effects

The present work is a numerical simulation of electroosmotic flow (EOF) in a cylindrical microchannel with the variation of wall surface charge (ζ -potential) distributions. The 2D Navier-Stoke equation governing the velocity field and the pressure are solved numerically using the finite element method (FEM). The numerical results show that the distorted electroosmotic velocity profiles and various kinds of flow circulation resulting from the axial variation of the ζ. The influences of heterogeneous patterns of zeta potential on the velocity profile, and the induced pressure distribution are discussed in this paper. This study shows that using heterogeneous patterns of zeta potential over the channel can generate local flow circulations and hence provide effective means to improve the mixing within the microchannels.