Wave equation for sums of squares on compact Lie groups
Wave equation for sums of squares on compact Lie groups
复制标题
DOI：
10.1016/j.jde.2015.01.034
复制
发表时间：
2014-03
影响因子：
2.4
通讯作者：
Claudia Garetto;Michael Ruzhansky
中科院分区：
文献类型：
--
作者：
Claudia Garetto;Michael Ruzhansky
本文研究了紧李群上向量场平方和波动方程的柯西问题的适定性。我们得到了局部Sobolev空间中Cauchy问题解的正则性损失，这取决于Hörmander条件满足的顺序，但在全局定义空间中没有损失。我们还建立了具有不规则系数和/或多重特征的方程的geevrey适定性。正如在Sobolev空间中一样，如果在局部坐标中表述，我们观察到局部Gevrey阶的损失，这取决于Hörmander条件满足的阶数。
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.