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Low-regularity Schrödinger maps. (English) Zbl 1212.35449

Summary: We prove that the Schrödinger map initial-value problem \(\partial _{t}s=s\times \Delta _{x}s\) on \(\mathbb R^d\times [-1,1]\), \(s(0)=s_0\) is locally well posed for small data \(s_0\in H_{Q}^{\sigma _0}(\mathbb R^d;\mathbb S^2)\), \(\sigma _0>(d+1)/2\), \(Q\in \mathbb S^2\).

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
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