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arXiv · 2408.14737

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

Yingzhe Ban·Minjie Shan
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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 $C^{1}$ at time $t$ in a null set containing all rational numbers, but are $C^{1}$ 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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Yingzhe Ban, Minjie Shan. 2024-08-27. Dispersive blow-up for solutions to three dimensional generalized Zakharov-Kuznetsov equations. https://arxiv.org/abs/2408.14737

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