Abstract
We prove that the Schrödinger map initial-value problem \begin{equation*} \begin{cases} & \partial_ts=s\times\Delta_x s\,\text{ on }\,\mathbb{R}^d\times[-1,1];\\ & s(0)=s_0 \end{cases} \end{equation*} is locally well posed for small data $s_0\in H^{{\sigma_0}}_Q(\mathbb{R}^d;\mathbb{S}^2)$, ${\sigma_0}>(d+1)/2$, $Q\in\mathbb{S}^2$.
Citation
Alexandru D. Ionescu. Carlos E. Kenig. "Low-regularity Schrödinger maps." Differential Integral Equations 19 (11) 1271 - 1300, 2006. https://doi.org/10.57262/die/1356050302
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