WIAS Preprint No. 3015, (2023)

A model of gravitational differentiation of compressible self-gravitating planets


Authors

  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Roubíček, Tomáš
    ORCID: 0000-0002-0651-5959
  • Stefanelli, Ulisse

2020 Mathematics Subject Classification

  • 35Q49 35Q74 65M60, 74A30, 74L10, 76N06, 76T30, 86A17

Keywords

  • Self-gravitating viscoelastic media, multi-component fluids, finite strains, Navier--Stokes--Poisson system, multipolar continua, gravitation, transport equations, Eulerian formulation, Galerkin approximation, weak solutions

DOI

10.20347/WIAS.PREPRINT.3015

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.

Download Documents