Dispersive blow-up for solutions to three dimensional generalized Zakharov-Kuznetsov equations

2024/08/27 by Yingzhe Ban, Ban, Yingzhe, Minjie Shan +1
Mathematics · Physics and Astronomy · #35B44 #35Q53 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2408.14737

openalex publication_date 2024/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We illustrate the dispersive blow up phenomena of the solutions of three dimensional generalized Zakharov-Kuznetsov equations. In particular, we construct smooth initial data such that, the associated global solutions fail to be C¹ at time t in a null set containing all rational numbers, but are C¹ at all times t which are generic irrational numbers. The key ingredient are to construct linear solutions which exhibit such phenomena and to prove nonlinear smoothing estimates for the full nonlinear model.

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