Well-posedness and stability of classical solutions to the multidimensional full hydrodynamic model for semiconductors

This paper is concerned with the global well-posedness and stability of classical solutions to the Cauchy problem for the multidimensional full hydrodynamic model in semiconductors on the framework of Besov space. By using the high- and low- frequency decomposition method, we obtain the exponential decay of classical solutions (close to equilibrium). Moreover, it is also shown that the vorticity decays to zero exponentially in the 2D and 3D space. The work weakens the regularity requirement of the initial data and improves some known results in Sobolev space.