Dynamical elastic bodies in Newtonian gravity
General Relativity and Quantum Cosmology
2012-06-28 v1
Abstract
Well-posedness for the initial value problem for a self-gravitating elastic body with free boundary in Newtonian gravity is proved. In the material frame, the Euler-Lagrange equation becomes, assuming suitable constitutive properties for the elastic material, a fully non-linear elliptic-hyperbolic system with boundary conditions of Neumann type. For systems of this type, the initial data must satisfy compatibility conditions in order to achieve regular solutions. Given a relaxed reference configuration and a sufficiently small Newton's constant, a neigborhood of initial data satisfying the compatibility conditions is constructed.
Cite
@article{arxiv.1106.3879,
title = {Dynamical elastic bodies in Newtonian gravity},
author = {Lars Andersson and Todd A. Oliynyk and Bernd G. Schmidt},
journal= {arXiv preprint arXiv:1106.3879},
year = {2012}
}