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Rough solutions for the wave maps equation
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 127, Number 2, April 2005
- pp. 293-377
- 10.1353/ajm.2005.0014
- Article
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We consider the wave maps equation with values into a Riemannian manifold which is isometrically embedded in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]. Our main result asserts that the Cauchy problem is globally well-posed for initial data which is small in the critical Sobolev spaces. This extends and completes recent work of Tao and other authors.