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

Capogna, Luca; Shatah, Jalal

doi:10.1090/S0002-9939-08-09302-7

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.

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