A note on ill-posedness of the Cauchy problem for Heisenberg wave maps
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- by Luca Capogna and Jalal Shatah PDF
- Proc. Amer. Math. Soc. 136 (2008), 1619-1629 Request permission
Abstract:
We introduce a notion of wave maps with a target in the sub-Riemannian Heisenberg group and study their relation with Riemannian wave maps with range in Lagrangian submanifolds. As an application we establish existence and eventually ill-posedness of the corresponding Cauchy problem.References
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Additional Information
- Luca Capogna
- Affiliation: Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701
- MR Author ID: 336615
- Email: lcapogna@comp.uark.edu
- Jalal Shatah
- Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer St., New York, New York 10012
- MR Author ID: 160000
- Email: shatah@cims.nyu.edu
- Received by editor(s): September 19, 2006
- Published electronically: January 28, 2008
- Additional Notes: The first author was partially supported by a National Science Foundation CAREER grant and by an Arkansas Science and Technology Authority grant.
The second author was partially supported by the National Science Foundation grant DMS 0203485. - Communicated by: David S. Tartakoff
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1619-1629
- MSC (2000): Primary 35L55, 53C17
- DOI: https://doi.org/10.1090/S0002-9939-08-09302-7
- MathSciNet review: 2373591