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

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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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2008-05, Vol.136 (5), p.1619-1629
Main Authors: Capogna, Luca, Shatah, Jalal
Format: Article
Language:English
Subjects:
Cauchy problem
Coefficients
Euler Lagrange equation
Exact sciences and technology
General mathematics
General, history and biography
Geodesy
Lagrangian function
Mathematics
Riemann manifold
Sciences and techniques of general use
Uniqueness
Vector fields
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Description
Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-08-09302-7