English

Blowing Up Solutions to the Zakharov System for Langmuir Waves

Analysis of PDEs 2019-07-02 v1

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.

Keywords

Cite

@article{arxiv.1907.00926,
  title  = {Blowing Up Solutions to the Zakharov System for Langmuir Waves},
  author = {Yuri Cher and Magdalena Czubak and Catherine Sulem},
  journal= {arXiv preprint arXiv:1907.00926},
  year   = {2019}
}

Comments

16 pages, 2 figures;