arXiv subjects

Hung Luong

Publications and source records attributed to Hung Luong.

3 recordsLinked to original sources

arXiv2025

Revisiting the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system

In this paper, we revisit the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system. Our method is based on the dispersive estimates and the suitable Bourgain's spaces. We then, obtain the local well-posedness of the solution with the main component $\psi$ belongs to $H^1(\mathbb{R}^d)$ ($d=2, 3$) which is actually the energy space corresponding to this component. Our result also suggests a potential approach to the problem of finding exact existence time scale for the solution of Benney-Roskes model in the context of water waves.

math.AP↗

arXiv2018

Local well-posedness for the Zakharov system on the background of a line soliton

We prove that the Cauchy problem for the two-dimensional Zakharov system is locally well-posed for initial data which are localized perturbations of a line solitary wave. Furthermore, for this Zakharov system, we prove weak convergence to a nonlinear Schrödinger equation.

math.AP↗

arXiv2018

On the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system

We address various issues concerning the Cauchy problem for the Zakharov-Rubenchik system (known as the Benney-Roskes system in water waves theory), which models the interaction of short and long waves in many physical situations. Motivated by the transverse stability/instability of the one-dimensional solitary wave (line solitary), we study the Cauchy problem in the background of a line solitary wave.

math.AP↗