Stability problem plays a fundamental role in the fluid study.A stable steady state is physically important for its observation,while instability of steady states is the source of complicated dynamic patterns which eventually may become turbulent.In general,it has been a challenging mathematical problem to find effective methods to characterize stability of a given steady state.In recent years,new variational methods and rigorous asymptotic analysis are developed to determine linear stability of viscous as well as inviscid steady flows.