Abstract
We consider the Cauchy problem for the generalized Thirring model $(\partial _t \pm \partial _x ) U_{\pm} = i |U_{\pm}|^k |U_{\mp}|^{m-k} U_{\pm}$ in one spatial dimension which was introduced in [4]. Several results on well-posedness and ill-posedness have been obtained. Since the nonlinearity is not smooth if $k$ or $m$ is odd, an upper bound of $s$ to be well-posed appears. We prove that the upper bound is essential. More precisely, we show ill-posedness in $H^s(\mathbb{R})$ for sufficiently large $s$ which is a novel feature of this paper.
Citation
Hyungjin Huh. Shuji Machihara. Mamoru Okamoto. "Well-posedness and ill-posedness of the Cauchy problem for the generalized Thirring model." Differential Integral Equations 29 (5/6) 401 - 420, May/June 2016. https://doi.org/10.57262/die/1457536884
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