Ill-posedness of the Thirring model below the critical regularity

Sigmund Selberg; Achenef Tesfahun

doi:10.1063/1.5124096

Ill-posedness of the Thirring model below the critical regularity

Analysis of PDEs 2020-08-26 v2

Authors: Sigmund Selberg , Achenef Tesfahun

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Abstract

We consider a nonlinear $L^2$ -critical nonlinear Dirac equation in one space dimension known as the Thirring model. Global well-posedness in $L^2$ for this equation was proved by Candy. Here we prove that the equation is ill posed in $L^p$ for $1 \le p < 2$ , and in the massless case also in $H^s$ with $s < 0$ .

Cite

@article{arxiv.1906.02251,
  title  = {Ill-posedness of the Thirring model below the critical regularity},
  author = {Sigmund Selberg and Achenef Tesfahun},
  journal= {arXiv preprint arXiv:1906.02251},
  year   = {2020}
}

Comments

Added references and a proof of non-existence of self-similar solutions in the massless case

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