3 citations · 6 across the 4 of their papers we have counts for
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Uniqueness of the solution to the Vlasov-Poisson system with bounded density
G. Loeper
In this note, we show uniqueness of weak solutions to the Vlasov-Poisson system on the only condition that the macroscopic density defined by $ρ(t,x) = \int_{\Rd} f(t,x,ξ)dξ$ i…
A fully non-linear version of the Euler incompressible equations: the semi-geostrophic system
G. Loeper
This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain co…
A geometric approximation to the Euler equations: the Vlasov-Monge-Ampere system
Yann Brenier, Gregoire Loeper
This paper studies the Vlasov-Monge-Ampere system (VMA), a fully non-linear version of the Vlasov-Poisson system (VP) where the (real) Monge-Ampere equation substitutes for the usu…
The Inverse Problem for the Euler-Poisson system in Cosmology
G. Loeper
The motion of a continuum of matter subject to gravitational interaction is classically described by the Euler-Poisson system. Prescribing the density of matter at initial and fina…