On the global evolution of self-gravitating matter. Nonlinear interactions in Gowdy symmetry

DOI10.1007/s00205-018-01354-5zbMath1416.83034arXiv1805.10278OpenAlexW3080433091WikidataQ64290341 ScholiaQ64290341MaRDI QIDQ1741803

Bruno Le Floch, Philippe G. LeFloch

Publication date: 7 May 2019

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.10278

zbMATH Keywords

Euler equationsnonlinear interactionGowdy symmetryself-gravitating matterglobal evolution

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) (83C55) PDEs in connection with relativity and gravitational theory (35Q75) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Approximation procedures, weak fields in general relativity and gravitational theory (83C25) Euler equations (35Q31)

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Cites Work

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• A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on \(T ^{3}\)
• On space-times with U(1)\(\times U(1)\) symmetric compact Cauchy surfaces
• Weakly regular \(T^2\)-symmetric spacetimes. The future causal geometry of Gowdy spacetimes
• Vacuum spacetimes with two-parameter spacelike isometry groups and compact invariant hypersurfaces: Topologies and boundary conditions
• Global solutions of the relativistic Euler equations
• Local smooth solutions of the relativistic Euler equation
• Self-gravitating relativistic fluids: A two-phase model
• Weakly regular Einstein-Euler spacetimes with Gowdy symmetry: the global areal foliation
• Global foliations of matter spacetimes with Gowdy symmetry
• Definition and stability of Lorentzian manifolds with distributional curvature
• The characteristic initial value problem for plane symmetric spacetimes with weak regularity
• Hyperbolic systems of conservation laws II
• Existence theory for nonlinear hyperbolic systems in nonconservative form
• Bounded variation solutions of the spherically symmetric einstein‐scalar field equations
• The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes
• On a wave map equation arising in general relativity
• On the Area of the Symmetry Orbits in Weakly Regular Einstein--Euler Spacetimes with Gowdy Symmetry
• Solutions in the large for nonlinear hyperbolic systems of equations
• THE SPACES $ BV$ AND QUASILINEAR EQUATIONS
• Hyperbolic Conservation Laws in Continuum Physics

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