A model of gravitational differentiation of compressible self-gravitating planets

TL;DR

This paper develops a comprehensive Eulerian model for inhomogeneous, self-gravitating viscoelastic media, including fluids and chemically reacting mixtures, with applications to planetary differentiation and phase transitions.

Contribution

It introduces a novel dynamic, Eulerian framework for modeling gravitational differentiation in inhomogeneous, viscoelastic planetary materials, extending to reactive multi-component fluids.

Findings

Proved existence and regularity of weak solutions for the model.

Extended the model to chemically reacting viscoelastic fluids.

Applied the model to planetary geophysics scenarios.

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.