A model of gravitational differentiation of compressible self-gravitating planets

Abstract

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.