On one dimensional Quantum Zakharov system

Abstract

In this paper, we discuss the properties of one dimensional quantum Zakharov system which describes the nonlinear interaction between the quantum Langmuir and quantum ion-acoustic waves. The system with initial data $(E(0),n(0),{\partial }_{t}n(0))\in H^k⨁H^l⨁H^{l-2}$ is local well posedness in low regularity spaces. Especially, the low regularity result for $k$ satisfies $-3/4<k\le -1/4$ is obtained by using the key observation that the convoluted phase function is convex and careful bilinear analysis. The result can not be obtained by using only Strichartz inequalities for "Schrödinger" waves.

We corrected many typos in previous version. The result is the same

References in corpus (2)

• Convolutions of singular measures and applications to the Zakharov system
• Quantum and classical dynamics of Langmuir wave packets

Cited by in corpus (2)

• Multilinear Weighted Estimates and Quantum Zakharov System
• Modified Strichartz Estimate of the Periodic Fourth Order NLS