The quasi-neutral limit of the multi-dimensional non-isentropic bipolar Euler-Poisson system is considered in the present paper. It is shown that for well-prepared initial data the smooth solution of the non-isentropic bipolar Euler-Poisson system converges strongly to the compressible non-isentropic Euler equations as the Debye length goes to zero.
We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the gradient of the velocity only, which coincides with the famous Beale-Kato-Majda criterion for ideal incompressible flows.
Seasonal variability of the bifurcation of the North Equatorial Current （NEC） is studied by constructing the analytic solu- tion for the time-dependent horizontal linear shallow water quasi-geostrophic equations. Using the Florida State University wind data from 1961 through 1992, we find that the bifurcation latitude of the NEC changes with seasons. Furthermore, it is shown that the NEC bifurcation is at its southernmost latitude （12.7°N） in June and the northernmost latitude （14.4~ N） in November.
