Global Well-posedness of the Adiabatic Limit of Quantum Zakharov System in 1D

Abstract

In this paper, we prove the low-regularity global well-posedness of the adibatic limit of the Quantum Zakharov system and consider its semi-classical limit, i.e., the convergence of the model equation as the quantum parameter tends to zero. We also show ill-posedness in negative Sobolev spaces and discuss the existence of ground-state soliton solutions in high spatial dimensions.