Well-posedness for the free boundary hard phase model in general relativity
DOI10.1016/j.aim.2024.109614arXiv2112.05285MaRDI QIDQ6126742
Shuang Miao, Sohrab Shahshahani
Publication date: 10 April 2024
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.05285
Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Free boundary problems for PDEs (35R35) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Equations of motion in general relativity and gravitational theory (83C10) Einstein equations (35Q76) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Dynamical compact elastic bodies in general relativity
- A priori estimates for relativistic liquid bodies
- Well posedness for the motion of a compressible liquid with free surface boundary
- Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum
- Partial differential equations. I: Basic theory
- Well-posedness in Sobolev spaces of the full water wave problem in 2D
- Self-gravitating relativistic fluids: A two-phase model
- The relativistic Euler equations with a physical vacuum boundary: Hadamard local well-posedness, rough solutions, and continuation criterion
- Well-posedness of free boundary hard phase fluids in Minkowski background and their Newtonian limit
- Local well-posedness for the motion of a compressible, self-gravitating liquid with free surface boundary
- On ``hard stars in general relativity
- Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires
- Relativistic Hydrodynamics
- On the existence of solutions to the relativistic Euler equations in two spacetime dimensions with a vacuum boundary
- Wellposedness and singularities of the water wave equations
- Local existence for the free boundary problem for nonrelativistic and Relativistic compressible Euler equations with a vacuum boundary condition
- Motion of isolated bodies
- On the free boundary problem of three-dimensional incompressible Euler equations
- The initial value problem for a class of general relativistic fluid bodies
- Well-posedness in Sobolev spaces of the full water wave problem in 3-D
- Initial-boundary value problem for the spherically symmetric Einstein equations for a perfect fluid
- A note on the relativistic Euler equations
- Hyperbolic reductions for Einstein's equations
- A priori estimates for a relativistic liquid with free surface boundary
- A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary
- Well-Posedness of the Free-Boundary Compressible 3-D Euler Equations with Surface Tension and the Zero Surface Tension Limit
- The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I
- Symmetric hyperbolic linear differential equations
