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Wave equation for sums of squares on compact Lie groups

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journal contribution
posted on 15.04.2015, 10:40 by Claudia Garetto, Michael Ruzhansky
In 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 Equations

Volume

258

Issue

12

Pages

4324 - 4347

Citation

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

2015-02-07

Notes

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

0022-0396

eISSN

1090-2732

Other identifier

S0022-0396(15)00046-7

Language

en

Licence

Exports

Read the paper on the publisher website

Loughborough Publications

Licence

Exports