Low Regularity Global Well-posedness for the Quantum Zakharov System in $1D$

Abstract

In this paper, we consider the quantum Zakharov system in one spatial dimension. We prove the global well-posedness of the system with $L^2$-Schrödinger data and some wave data. The regularity of the wave data is in the largest set. We give counterexamples for the boundary of the set. As the quantum parameter tends to zero, we formally recover the result of Colliander-Holmer-Tzirakis for the classical Zakharov system.