Blowing Up Solutions to the Zakharov System for Langmuir Waves
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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