Abstract. The well-posedness of smooth solution to a 3-D simplified Energy-Transport model is discussed in this paper. We prove the local existence, uniqueness, and asymptotic behavior of solution to the equations with hybrid cross-diffusion. The smooth solution convergences to a stationary solution with an exponential rate as time tends to infinity when the initial date is a small perturbation of the stationary solution.

The quasineutral limit and the mixed layer problem of a three-dimensional drift-diffusion model is discussed in this paper. For the Neumann boundaries and the general initial data, the quasineutral limit is proven rigorously with the help of the weighted energy method, the matched asymptotic expansion method of singular perturbation problem and the entropy production inequality.