Wave equation for sums of squares on compact Lie groups

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:258

Article

Garetto, Claudia¹  Ruzhansky, Michael² 

[1] Univ Loughborough, Dept Math Sci, Loughborough LE11 3TU, Leics, England

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

关键词: Wave equation;    Sub-Laplacian;    Sum of squares;    Well-posedness;    Sobolev spaces;    Gevrey spaces;   

DOI  :  10.1016/j.jde.2015.01.034

来源: Elsevier

【 摘 要 】

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. (C) 2015 The Authors. Published by Elsevier Inc.

【 授权许可】

Free