285 citations · 682 across the 44 of their papers we have counts for
12 papers · 1 filter
A simple proof of non-explosion for measure solutions of the Keller-Segel equation
Nicolas Fournier, Yoan Tardy
We give a simple proof, relying on a {\it two-particles} moment computation, that there exists a global weak solution to the -dimensional parabolic-elliptic Keller-Segel equatio…
A non-expanding transport distance for some structured equations
Nicolas Fournier, Benoît Perthame
Structured equations are a standard modeling tool in mathematical biology. They areintegro-differential equations where the unknown depends on one or several variables, representin…
On exponential moments of the homogeneous Boltzmann equation for hard potentials without cutoff
Nicolas Fournier
We consider the spatially homogeneous Boltzmann equation for hard potentials without cutoff. We prove that an exponential moment of order , with the usual not…
Stability, well-posedness and regularity of the homogeneous Landau equation for hard potentials
Nicolas Fournier, Daniel Heydecker
We establish the well-posedness and some quantitative stability of the spatially homogeneous Landau equation for hard potentials, using some specific Monge-Kantorovich cost, assumi…
Monge-Kantorovich distance for PDEs: the coupling method
Nicolas Fournier, Benoît Perthame
We informally review a few PDEs for which the Monge-Kantorovich distance between pairs of solutions, possibly with some judicious cost function, decays: heat equation, Fokker-Planc…
A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff
Nicolas Fournier
We consider the spatially homogeneous Boltzmann equation for hard potentials with angular cutoff. This equation has a unique conservative weak solution , once the…