可压缩自引力行星的引力分异模型
A model of gravitational differentiation of compressible self-gravitating planets
AI总结：
该研究提出一个有限应变下非均匀粘弹性介质的动力学模型，采用Kelvin-Voigt流变学和欧拉方法，证明弱解存在性，并扩展到多组分化学反应流体，用于描述行星引力分异及体积相变。
摘要：
我们提出了一个有限应变下非均匀粘弹性介质的动力学模型。该模型采用Kelvin-Voigt流变学，并在实际演化构型中包含自产生的引力场。特别地，我们采用了完全欧拉方法。我们将该模型专门化到粘弹性（正压）流体，并通过Faedo-Galerkin半离散化技术证明了全局弱解的存在性和一定的正则性。然后，基于Eckart和Prigogine的现象学方法，我们提出并研究了对多组分化学反应粘弹性流体的扩展。该模型受行星地球物理学的启发。特别是，它描述了非均匀行星和卫星的引力分异，这些天体可能经历体积相变。
英文摘要：
We present a dynamic model for inhomogeneous viscoelastic media at finite strains. The model features a Kelvin-Voigt rheology, and includes a self-generated gravitational field in the actual evolving configuration. In particular, a fully Eulerian approach is adopted. We specialize the model to viscoelastic (barotropic) fluids and prove existence and a certain regularity of global weak solutions by a Faedo-Galerkin semi-discretization technique. Then, an extension to multi-component chemically reacting viscoelastic fluids based on a phenomenological approach by Eckart and Prigogine, is advanced and studied. The model is inspired by planetary geophysics. In particular, it describes gravitational differentiation of inhomogeneous planets and moons, possibly undergoing volumetric phase transitions.
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