阻尼时谐Galbrun方程和恒星振动方程的适定性
On the well-posedness of the damped time-harmonic Galbrun equation and the equations of stellar oscillations
摘要：
我们研究了时谐Galbrun方程描述的声音在存在一个稳定的背景流的传播。加上旋转和引力项，这些方程在日震学和星震学中也是基本的恒星振荡模型。对于一个简单的阻尼模型，我们证明了这些方程的适定性，即唯一性，存在性和稳定性的解决方案在温和的条件下的参数（基本上亚音速流动）。我们分析的主要工具是广义亥姆霍兹分解。
英文摘要：
We study the time-harmonic Galbrun equation describing the propagation of sound in the presence of a steady background flow. With additional rotational and gravitational terms these equations are also fundamental in helio- and asteroseismology as a model for stellar oscillations. For a simple damping model we prove well-posedness of these equations, i.e. uniqueness, existence, and stability of solutions under mild conditions on the parameters (essentially subsonic flows). The main tool of our analysis is a generalized Helmholtz decomposition.
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