The $L^2$ contraction of solutions with large perturbation in multiple space dimensions from the oscillatory dispersive planar shock

Abstract

In this paper, we show the $L^2$ contraction property of the planar oscillatory or monotone dispersive shock profiles of the dissipative Kadomtsev-Petviashvili (KP) equation modelling water waves and the multi-dimensional Korteweg-de Vries (KdV) Burgers equation under arbitrarily large perturbations in two space dimensions, up to Lipschitz time-dependent shifts. This stability result extends the results of two recent papers by Chen, Eun, Kang, and Shen on $L^2$ contraction for the KdV-Burgers equation.