Well-posednesss of strongly dispersive two-dimensional surface waves Boussinesq systems

TL;DR

This paper investigates the mathematical well-posedness of two-dimensional dispersive Boussinesq systems modeling weakly nonlinear long surface waves, focusing on the strongly dispersive KdV-KdV system.

Contribution

It establishes well-posedness results for the strongly dispersive two-dimensional Boussinesq systems, especially the KdV-KdV extension, which was previously less understood.

Findings

Proved well-posedness for the KdV-KdV system

Analyzed the dispersive properties of the two-dimensional Boussinesq models

Extended classical results to a vector two-dimensional setting

Abstract

We consider in this paper the well-posedness for the Cauchy problem associated to two-dimensional dispersive systems of Boussinesq type which model weakly nonlinear long wave surface waves. We emphasize the case of the {\it strongly dispersive} ones with focus on the "KdV-KdV" system which possesses the strongest dispersive properties and which is a vector two-dimensional extension of the classical KdV equation.