Dynamical elastic bodies in Newtonian gravity
arXiv:1106.3879 · doi:10.1088/0264-9381/28/23/235006
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.
References in corpus (8)
- Well posedness for the motion of a compressible liquid with free surface boundary
- Motion of Isolated bodies
- Static self-gravitating elastic bodies in Einstein gravity
- The Newtonian limit for perfect fluids
- Celestial mechanics of elastic bodies
- Local existence for the free boundary problem for the non-relativistic and relativistic compressible Euler equations with a vacuum boundary condition
- A priori estimates for the motion of a self-gravitating incompressible liquid with free surface boundary
- Well-posedness of compressible Euler equations in a physical vacuum