From the 1 of 8 linked papers with an AI index.
8 papers
Harmonic, radial, and shell stability of the weighted Einstein constraints on the sphere at infinity
Bruno Le Floch, Philippe G. LeFloch
We consider fourth-order and second-order partial differential operators localized on domains of the sphere in arbitrary dimension. These operators arise as weighted compositions o…
Physics-informed token transformer methodology for nonlinear balance laws. I. Schwarzschild--Burgers fluid flows
Philippe G. LeFloch, Shuyang Xiang
We introduce a Physics-Informed Token Transformer (PITT) methodology for nonlinear hyperbolic balance laws in one space dimension, using piecewise steady-state profiles for the rep…
Stability and instability of torus-symmetric Einstein spacetimes with square-integrable connection
Bruno Le Floch, Philippe G. LeFloch
We study the global evolution problem for the Einstein equations under T2 symmetry on T3, allowing vacuum, scalar-field, and compressible-fluid matter models, governed by a general…
Scattering laws for interfaces in self-gravitating matter flows
Bruno Le Floch, Philippe G. LeFloch
We consider the evolution of self-gravitating matter fields that may undergo phase transitions, and we connect ideas from phase transition dynamics with concepts from bouncing cosm…
A first-order formulation of f(R) gravity in spherical symmetry
Philippe G. LeFloch, Filipe C. Mena
We develop an augmented characteristic, first-order formulation of the field equations in f(R) gravity governing the global evolution of a (possibly) massive scalar field phi under…
The global nonlinear stability of Minkowski spacetime with self-gravitating massive Dirac fields
Philippe G. LeFloch, Yue Ma, Weidong Zhang
We consider the Einstein-Dirac system for a massive field, which describes the evolution of self-gravitating massive spinor fields, and we investigate the global evolution problem,…