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A note on ill-posedness of the Cauchy problem for Heisenberg wave maps


Authors: Luca Capogna and Jalal Shatah
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
Published electronically: January 28, 2008
MathSciNet review: 2373591
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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.


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Additional Information

Luca Capogna
Affiliation: Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701
Email: lcapogna@comp.uark.edu

Jalal Shatah
Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer St., New York, New York 10012
Email: shatah@cims.nyu.edu

DOI: https://doi.org/10.1090/S0002-9939-08-09302-7
Keywords: Wave maps, Heisenberg group
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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