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Wave equation for sums of squares on compact Lie groups
journal contribution
posted on 2015-04-15, 10:40 authored by Claudia Garetto, Michael RuzhanskyIn this paper we investigate the well-posedness of the Cauchy problem for the wave equation for sums of squares of vector fields on compact Lie groups. We obtain the loss of regularity for solutions to the Cauchy problem in local Sobolev spaces depending on the order to which the Hörmander condition is satisfied, but no loss in globally defined spaces. We also establish Gevrey well-posedness for equations with irregular coefficients and/or multiple characteristics. As in the Sobolev spaces, if formulated in local coordinates, we observe well-posedness with the loss of local Gevrey order depending on the order to which the Hörmander condition is satisfied.
Funding
Open Access funded by Engineering and Physical Sciences Research Council
History
School
- Science
Department
- Mathematical Sciences
Published in
Journal of Differential EquationsVolume
258Issue
12Pages
4324 - 4347Citation
GARETTO, C. and RUZHANSKY, M., 2015. Wave equation for sums of squares on compact Lie groups. Journal of Differential Equations, 258 (12), pp. 4324–4347.Publisher
© The Authors. Published by Elsevier Inc.Version
- VoR (Version of Record)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/Publication date
2015-02-07Notes
This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Full details of the CC BY licence are available at: http://creativecommons.org/licenses/by/4.0/ISSN
0022-0396eISSN
1090-2732Publisher version
Other identifier
S0022-0396(15)00046-7Language
- en