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Journal Article

Dynamical elastic bodies in Newtonian gravity

MPS-Authors
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Andersson,  Lars
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Schmidt,  Bernd G.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1106.3879
(Preprint), 343KB

CQG_28_23_235006.pdf
(Any fulltext), 398KB

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Citation

Andersson, L., Oliynyk, T. A., & Schmidt, B. G. (2011). Dynamical elastic bodies in Newtonian gravity. Classical and quantum gravity, 28: 235006. doi:10.1088/0264-9381/28/23/235006.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000E-EA1B-6
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.