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arXiv · 1907.00926

Blowing Up Solutions to the Zakharov System for Langmuir Waves

Yuri Cher·Magdalena Czubak·Catherine Sulem
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Abstract

Langmuir waves take place in a quasi-neutral plasma and are modeled by the Zakharov system. The phenomenon of collapse, described by blowing up solutions plays a central role in their dynamics. We present in this article a review of the main mathematical properties of blowing up solutions. They include conditions for blowup in finite or infinite time, description of self-similar singular solutions and lower bounds for the rate of blowup of certain norms associated to the solutions.

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Yuri Cher, Magdalena Czubak, Catherine Sulem. 2019-07-01. Blowing Up Solutions to the Zakharov System for Langmuir Waves. https://arxiv.org/abs/1907.00926

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