Ill-posedness of the Thirring model below the critical regularity

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 $s<0$.

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

References in corpus (1)

• The cubic Dirac equation: Small initial data in $H^{\frac{1}{2}}({\mathbb{R}}^2)$