In this talk we discuss the stability and  instability of the steady state $(0,p_s)$ for the 3D incompressible viscous flow in a smooth bounded simply connected domain with Navier boundary condition. It is shown that there exists a critical slip friction coefficient $C_r \mu$ such that if the slip friction coefficient $\zeta$ is less than $C_r \mu$, then the steady state $({0,p_s)$ is linearly and nonlinearly unstable and conversely, for the case $\zeta>-C_r \mu$, the steady state $(0,p_s)$ is linearly and nonlinearly stable. We also present some results on stability/instability of the viscous incompressible capillary fluids.

会议密码:1013