The asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors

In this paper we study the asymptotic behavior of globally smooth solutions of the Cauchy problem for the multidimensional isentropic hydrodynamic model for semiconductors in Rd. We prove that smooth solutions (close to equilibrium) of the problem converge to a stationary solution exponentially fast as t→+∞.