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arXiv · 2407.18619

Singularity formation of hydromagnetic waves in cold plasma

Junsik Bae·Junho Choi·Bongsuk Kwon
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Abstract

We study $C^1$ blow-up of the compressible fluid model introduced by Gardner and Morikawa, which describes the dynamics of a magnetized cold plasma. We propose sufficient conditions that lead to $C^1$ blow-up. In particular, we find that smooth solutions can break down in finite time even if the gradient of initial velocity is identically zero. The density and the gradient of the velocity become unbounded as time approaches the lifespan of the smooth solution. The Lagrangian formulation reduces the singularity formation problem to finding a zero of the associated second-order ODE.

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Junsik Bae, Junho Choi, Bongsuk Kwon. 2024-07-26. Singularity formation of hydromagnetic waves in cold plasma. https://arxiv.org/abs/2407.18619

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