2 citations · 3 across the 7 of their papers we have counts for
7 papers
Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity
Philippe G. LeFloch, Cristinel Mardare, Sorin Mardare
Assuming minimal regularity assumptions on the data, we revisit the classical problem of finding isometric immersions into the Minkowski spacetime for hypersurfaces of a Lorentzian…
Definition and stability of Lorentzian manifolds with distributional curvature
Philippe G. LeFloch, Cristinel Mardare
Following Geroch, Traschen, Mars and Senovilla, we consider Lorentzian manifolds with distributional curvature tensor. Such manifolds represent spacetimes of general relativity tha…
Zero diffusion-dispersion limits for scalar conservation laws
Cezar Kondo, Philippe G. LeFloch
We consider solutions of hyperbolic conservation laws regularized with vanishing diffusion and dispersion terms. Following a pioneering work by Schonbek, we establish the convergen…
The hyperbolic mean curvature flow
Philippe G. LeFloch, Knut Smoczyk
We introduce a geometric evolution equation of hyperbolic type, which governs the evolution of a hypersurface moving in the direction of its mean curvature vector. The flow stems f…
Hyperbolic conservation laws and spacetimes with limited regularity
Philippe G. LeFloch
Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to…
Entropy solutions of the Euler equations for isothermal relativistic fluids
Philippe G. LeFloch, Mitsuru Yamazaki
We investigate the initial-value problem for the relativistic Euler equations governing isothermal perfect fluid flows, and generalize an approach introduced by LeFloch and Shelukh…