Dynamical elastic bodies in Newtonian gravity

Details Dynamical elastic bodies in Newtonian gravity Dynamical elastic bodies in Newtonian gravity

2011-06-20

arxiv.org/abs/1106.3879v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

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.

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