Global existence and the algebraic decay rate of the solution for the quantum Navier–Stokes–Poisson equations in R3

Abstract

The Cauchy problem of compressible quantum Navier–Stokes–Poisson equations in three-dimensional space is considered in this paper. Under some smallness conditions on the initial data, we derive the existence of the global classical solution near the non-constant steady state by using the energy method. Combining the linear decay rate and the energy method, we also prove the algebraic decay rate of the solution toward the non-constant steady state with a small doping profile.