I wrote with Luis Silvestre (University of Chicago) a series of articles about the Boltzmann equation without cut-off in the inhomogeneous case. The goal was to prove C∞ a priori estimates for solutions of the inhomogeneous Boltzmann equation without cut-off, conditional to point-wise bounds on their mass, energy and entropy densities. The final paper is … Lire la suite
In collaboration with F. Golse, M. P. Gualdani and A. F. Vasseur. It can be found in the hal and also in arxiv. Abstract: We prove that the set of singular times for weak solutions of the space homogeneous Landau equation with Coulomb potential constructed as in [C. Villani, Arch. Rational Mech. Anal. 143 (1998), … Lire la suite
Together with C. Mouhot and L. Silvestre, we just uploaded on hal and arxiv a new preprint entitled Gaussian lower bounds for the Boltzmann equation. Abstract: The study of positivity of solutions to the Boltzmann equation goes back to Carleman (1933), and the initial argument of Carleman was developed byPulvirenti-Wennberg (1997), the second author and … Lire la suite
A new preprint entitled « The Schauder estimate for kinetic integral equations » is available on arxiv and hal. This is a joint work with Luis Silvestre. Abstract: We establish interior Schauder estimates for kinetic equations with integro-differential diffusion. We study equations of the form ft+v⋅∇xf=Lvf+c, where Lv is an integro-differential diffusion operator of order 2s acting … Lire la suite
A conference entitled Non stantard diffusions in fluids, kinetic equations and probability will take place in Marseille at the Centre international de rencontres mathématiques. This conference aims at bringing together experts from different subjects in mathematics that share the common theme of nonlocal diffusions, building bridges between these communities and fostering collaboration. From the probabilistic … Lire la suite
A workshop entitled From Optimal Control to Maximum Principle will be held in Agropoli next September (12-14) on the occasion of Italo Capuzzo Dolcetta‘s birthday. The aim of the workshop is to bring together researchers from Italy and from abroad working on themes that are present in the research activity of Italo Capuzzo Dolcetta, such … Lire la suite
Starting from August 2018, I will spend one year in the Institudo de Matemática Pura e Aplicada (IMPA), located in Rio de Janeiro, Brasil. IMPA is a worldwide renowned Mathematical sciences research institute which plays a leading role in Brazil and Latin America due to its research excellence, as well as its role in the … Lire la suite
C. Mouhot, L. Silvestre and myself just uploaded on HAL and arXiv a new preprint entitled Decay estimates for large velocities in the Boltzmann equation without cut-off. Abstract: We establish pointwise large velocity decay rates for the solution of the inhomogeneous Boltzmann equation without cutoff, under the assumption that three hydrodynamic quantities (mass, energy, entropy … Lire la suite
There is a one-day workshop next week in Bologna about viscosity and variational solutions of nonlinear PDEs. It is organised by Fausto Ferrari and Fabiana Leoni.
A conference entitled Non stantard diffusions in fluids, kinetic equations and probability will take place in Marseille at the Centre international de rencontres mathématiques. This conference aims at bringing together experts from different subjects in mathematics that share the common theme of nonlocal diffusions, building bridges between these communities and fostering collaboration. From the probabilistic … Lire la suite
