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Dynamical elastic bodies in Newtonian gravity

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons20682

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;

Externe Ressourcen
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Volltexte (frei zugänglich)

1106.3879
(Preprint), 343KB

CQG_28_23_235006.pdf
(beliebiger Volltext), 398KB

Ergänzendes Material (frei zugänglich)
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Zitation

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.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000E-EA1B-6
Zusammenfassung
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.