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Title: Wave equation for sums of squares on compact Lie groups
Authors: Garetto, Claudia
Ruzhansky, Michael
Keywords: Gevrey spaces
Sobolev spaces
Sub-Laplacian
Sum of squares
Wave equation
Well-posedness
Issue Date: 2014
Publisher: © The Authors. Published by Elsevier Inc.
Citation: GARETTO, C. and RUZHANSKY, M., 2014. Wave equation for sums of squares on compact Lie groups. Journal of Differential Equations, 258 (12), pp. 4324–4347.
Abstract: 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.
Description: 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/
Sponsor: Open Access funded by Engineering and Physical Sciences Research Council
Version: Published
DOI: 10.1016/j.jde.2015.01.034
URI: https://dspace.lboro.ac.uk/2134/17278
Publisher Link: http://dx.doi.org/10.1016/j.jde.2015.01.034
ISSN: 0022-0396
Appears in Collections:Published Articles (Maths)

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