250 citations · 1.1k across the 130 of their papers we have counts for
7 papers · 2 filters
Weakly regular fluid flows with bounded variation on a Schwarzschild background
Philippe G. LeFloch, Shuyang Xiang
We study the global dynamics of isothermal fluids evolving in the domain of outer communication of a Schwarzschild black hole. We first formulate the initial value problem within a…
A central-upwind geometry-preserving method for hyperbolic conservation laws on the sphere
Abdelaziz Beljadid, Philippe G. LeFloch
We introduce a second-order, central-upwind finite volume method for the discretization of nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. The semi-disc…
Structure-preserving shock-capturing methods: late-time asymptotics, curved geometry, small-scale dissipation, and nonconservative products
Philippe G. LeFloch
We present some recent developments on shock capturing methods for nonlinear hyperbolic systems of balance laws, whose prototype is the Euler system of compressible fluid flows, an…
The relativistic Burgers equation on a FLRW background and its finite volume approximation
Tuba Ceylan, Philippe G. LeFloch, Baver Okutmustur
A relativistic generalization of the inviscid Burgers equation was proposed by LeFloch, Makhlof, and Okutmustur and then investigated on a Schwarzschild background. Here, we extend…
Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum
Juhi Jang, Philippe G. LeFloch, Nader Masmoudi
We study the evolution of a compressible fluid surrounded by vacuum and introduce a new symmetrization in Lagrangian coordinates that allows us to encompass both relativistic and n…
The global nonlinear stability of Minkowski space for the Einstein equations in presence of a massive field
Philippe G. LeFloch, Yue Ma
We provide a significant extension of the Hyperboloidal Foliation Method introduced by the authors in 2014 in order to establish global existence results for systems of quasilinear…