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Low-regularity Schrödinger maps, II: global well-posedness in dimensions d ≥  3

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Abstract

In dimensions d ≥ 3, we prove that the Schrödinger map initial-value problem

$$ \left\{ \begin{array}{l} \partial_ts=s\times\Delta_x s\hbox{ on }\mathbb{R}^d\times\mathbb{R};\\ s(0)=s_0 \end{array} \right. $$

is globally well-posed for small data s 0 in the critical Besov spaces \({\dot{B}_Q^{d/2}(\mathbb{R}^d;\mathbb{S}^2)}\), \({Q\in\mathbb{S}^2}\).

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin–Madison, Madison, WI, 53706, USA

    Alexandru D. Ionescu

  2. Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL, 60637-1514, USA

    Carlos E. Kenig

Authors
  1. Alexandru D. Ionescu
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  2. Carlos E. Kenig
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Corresponding author

Correspondence to Alexandru D. Ionescu.

Additional information

Communicated by P. Constantin

The first author was supported in part by an NSF grant and a Packard fellowship.

The second author was supported in part by an NSF grant.

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Ionescu, A.D., Kenig, C.E. Low-regularity Schrödinger maps, II: global well-posedness in dimensions d ≥  3. Commun. Math. Phys. 271, 523–559 (2007). https://doi.org/10.1007/s00220-006-0180-4

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  • DOI: https://doi.org/10.1007/s00220-006-0180-4

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