Asymptotic Stability Of Solutions To The Bipolar Hydrodynamic Model For Semiconductors

This paper is considered with the Cauchy problem for the multidimensional bipolar hydrodynamic model for semiconductors.Using the Littlewood-Paley decomposition and energy estimates,we obtain the global well-posedness and exponential stability of the classical solutions on the framework of Besov spaces.As a by-product,we prove that the vorticity of the velocity decays exponentially to0 in the 2D and 3D space.This paper is organized as follows.Firstly,we introduce the research progress of hydrodynamic model for semiconductors in recent years.In the preliminary knowledge,we introduce the definition and properties of the Littlewood-Paley decomposition and Besov space theory.Next,we reformulate the bipolar hydrodynamic model for semiconductors into symmetric hyperbolic system,and use the classical theory to obtain the local existence of the solutions.Lastly,Using the Littlewood-Paley decomposition and energy estimates,we obtain the crucial a priori estimates,thus the global existence of the classical solution and the exponential decay of the vorticity are obtained.