The L² contraction of solutions with large perturbation in multiple space dimensions from the oscillatory dispersive planar shock

2026/07/29 by Geng Chen, Harish Ravichandar, Yannan Shen
Mathematics · #math.AP

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arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

In this paper, we show the L² 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 L² contraction for the KdV-Burgers equation.

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