Global well-posedness to the 1D compressible quantum Navier–Stokes–Poisson equations with large initial data

Abstract

This paper is concerned with the global existence and large time behavior of classical solutions away from vacuum to the Cauchy problem of the 1D compressible quantum Navier–Stokes–Poisson equations with large initial perturbation. Moreover, we obtain the global strong/classical solution of Navier–Stokes–Poisson equations through the vanishing dispersion limit with certain convergence rates. We focus on the case that the viscosity depends on density linearly which extends the former results of constant viscosity in Zhang et al. (2022) by the second author. Some useful estimates are developed to deduce the uniform-in-time lower and upper bounds on the specific volume and the electric potential.