Wave equation for sums of squares on compact Lie groups
Claudia Garetto
Michael Ruzhansky
2134/17278
https://repository.lboro.ac.uk/articles/journal_contribution/Wave_equation_for_sums_of_squares_on_compact_Lie_groups/9387101
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.
2015-04-15 10:40:48
Gevrey spaces
Sobolev spaces
Sub-Laplacian
Sum of squares
Wave equation
Well-posedness
Mathematical Sciences not elsewhere classified