Abstract 

In this talk, I will report two aspects of work. One is about a class of new generalized Poisson-Nernst-Planck-Navier-Stokes equations. The other part involves a class of hydrodynamic equations for semiconductors. I will give the global well-posedness analysis of their three-dimensional Cauchy problems. In particular, I will introduce some detailed analyses on large non-constant stationary solutions of semiconductor equations.