6 papers · 1 filter
Propagation of chaos for the homogeneous Boltzmann equation with moderately soft potentials
Nicolas Fournier, Stéphane Mischler
We show that the Kac particle system converges, as the number of particles tends to infinity, to the solution of the homogeneous Boltzmann equation, in the regime of moderately sof…
On the Krein-Rutman theorem and beyond
Claudia Fonte Sanchez, Pierre Gabriel, Stéphane Mischler
In this work, we revisit the Krein-Rutman theory for semigroups of positive operators in a Banach lattice framework and we provide some very general, efficient and handy results wi…
The Kinetic Fokker-Planck equation in a domain: Ultracontractivity, hypocoercivity and long-time asymptotic behavior
Kleber Carrapatoso, Stéphane Mischler
We consider the Kinetic Fokker-Planck (FKP) equation in a domain with Maxwell reflection condition on the boundary. We establish the ultracontractivity of the associated semigroup…
On the self-similar stability of the parabolic-parabolic Keller-Segel equation
Frank Alvarez Borges, Kleber Carrapatoso, Stéphane Mischler
We consider the parabolic-parabolic Keller-Segel equation in the plane and prove the nonlinear exponential stability of the self-similar profile in a quasi parabolic-elliptic regim…
The Landau equation in a domain
Kleber Carrapatoso, Stéphane Mischler
This work deals with the Landau equation in a bounded domain with the Maxwell reflection condition on the boundary for any (possibly smoothly position dependent) accommodation coef…
Special macroscopic modes and hypocoercivity
Kleber Carrapatoso, Jean Dolbeault, Frédéric Hérau +3
We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and…