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Langmuir waves take place in a quasi-neutral plasma and are modeled by theZakharov system. The phenomenon of collapse, described by blowing up solutionsplays a central role in their dynamics. We present in this article a review ofthe main mathematical properties of blowing up solutions. They includeconditions for blowup in finite or infinite time, description of self-similarsingular solutions and lower bounds for the rate of blowup of certain normsassociated to the solutions.

Blowing Up Solutions to the Zakharov System for Langmuir Waves