Wave equation for sums of squares on compact Lie groups
- Author
- Claudia Garetto and Michael Ruzhansky (UGent)
- Organization
- 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 Hormander 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 Hormander condition is satisfied.
- Keywords
- Wave equation, Sub-Laplacian, Sum of squares, Well-posedness, Sobolev spaces, Gevrey spaces, PARTIAL-DIFFERENTIAL EQUATIONS, HYPERBOLIC-EQUATIONS, HOMOGENEOUS SPACES, HEISENBERG-GROUP, CAUCHY-PROBLEM, OPERATORS, COEFFICIENTS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8585206
- MLA
- Garetto, Claudia, and Michael Ruzhansky. “Wave Equation for Sums of Squares on Compact Lie Groups.” JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 258, no. 12, 2015, pp. 4324–47, doi:10.1016/j.jde.2015.01.034.
- APA
- Garetto, C., & Ruzhansky, M. (2015). Wave equation for sums of squares on compact Lie groups. JOURNAL OF DIFFERENTIAL EQUATIONS, 258(12), 4324–4347. https://doi.org/10.1016/j.jde.2015.01.034
- Chicago author-date
- Garetto, Claudia, and Michael Ruzhansky. 2015. “Wave Equation for Sums of Squares on Compact Lie Groups.” JOURNAL OF DIFFERENTIAL EQUATIONS 258 (12): 4324–47. https://doi.org/10.1016/j.jde.2015.01.034.
- Chicago author-date (all authors)
- Garetto, Claudia, and Michael Ruzhansky. 2015. “Wave Equation for Sums of Squares on Compact Lie Groups.” JOURNAL OF DIFFERENTIAL EQUATIONS 258 (12): 4324–4347. doi:10.1016/j.jde.2015.01.034.
- Vancouver
- 1.Garetto C, Ruzhansky M. Wave equation for sums of squares on compact Lie groups. JOURNAL OF DIFFERENTIAL EQUATIONS. 2015;258(12):4324–47.
- IEEE
- [1]C. Garetto and M. Ruzhansky, “Wave equation for sums of squares on compact Lie groups,” JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 258, no. 12, pp. 4324–4347, 2015.
@article{8585206,
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 Hormander 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 Hormander condition is satisfied.}},
author = {{Garetto, Claudia and Ruzhansky, Michael}},
issn = {{0022-0396}},
journal = {{JOURNAL OF DIFFERENTIAL EQUATIONS}},
keywords = {{Wave equation,Sub-Laplacian,Sum of squares,Well-posedness,Sobolev spaces,Gevrey spaces,PARTIAL-DIFFERENTIAL EQUATIONS,HYPERBOLIC-EQUATIONS,HOMOGENEOUS SPACES,HEISENBERG-GROUP,CAUCHY-PROBLEM,OPERATORS,COEFFICIENTS}},
language = {{eng}},
number = {{12}},
pages = {{4324--4347}},
title = {{Wave equation for sums of squares on compact Lie groups}},
url = {{http://doi.org/10.1016/j.jde.2015.01.034}},
volume = {{258}},
year = {{2015}},
}
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