Global Solutions And Large Time Behavior Of The Semiconductor Bipolar Quantum Hydrodynamic Equations

In this paper wo study the initial boundary value problems on the semiconductor multidimensional bipolar quantum hydrodynamic model. This model is a. system of the Euleriau equations with Bohm potential terms (third order derivatives) coupled with the Poisson equations, In the case of irrotational fluids, based on the nonlinear Schrodinger-Poisson system and the semigroup theory of linear operators, we proved the existence of local-in-time solutions with large initial values. In terms of the method of energy estimates, we obtain the exponential decay estimates, the global existence of solutions and their convergences to the corresponding steady state solutions exponentially if the initial value is close enough to a steady state solution.