arXiv subjects

Côme Tabary

Publications and source records attributed to Côme Tabary.

6 recordsLinked to original sources

arXiv2026

On the monotonicity of the entropy production in the Landau-Maxwell equation

We study the homogeneous Landau equation with Maxwell molecules and prove that the entropy production is non-increasing when the directional temperatures are well-distributed. It implies that for any initial condition with finite mass and energy, the entropy production is guaranteed to be non-increasing after a certain explicit time. We also obtain exponential decay of the entropy production. We provide an explicit formula for the derivative of the entropy production which may be a starting point for future progress towards full monotonicity.

math.AP↗

arXiv2026

Propagation of chaos for the Boltzmann equation with very soft potentials

We build solutions to Kac's particle system and show that their empirical measures converge to the solution of the space-homogeneous Boltzmann equation in the regime of very soft potentials. This proves propagation of chaos for the last class of kernels for which it was still open. The proof relies on new estimates on the dissipation of the Fisher information along the Boltzmann equation, which allow us to control the strong singularities of the system. These estimates are obtained thanks to a new inequality related to the fractional heat flow on the sphere, that might be of independent interest.

math.AP↗

arXiv2026

Propagation of chaos for the Landau equation with very soft and Coulomb potentials

We consider a drift-diffusion process of $N$ stochastic particles and show that its empirical measure converges, as $N\rightarrow \infty$, to the solution of the Landau equation. We work in the regime of very soft and Coulomb potentials using a tightness/uniqueness method. To claim uniqueness, we need high integrability estimates that we obtain by crucially exploiting the dissipation of the Fisher information at the level of the particle system. To be able to exploit these estimates as $N\rightarrow \infty$, we prove the affinity in infinite dimension of the entropy production and Fisher information dissipation (and other first and second-order versions of the Fisher information through a general theorem), results which were up to now only known for the entropy and the usual Fisher information.

math.AP↗

arXiv2025

Weak-strong uniqueness for the Landau equation by a relative entropy method

We derive a weak-strong uniqueness and stability principle for the Landau equation in the soft potentials case (including Coulomb interactions). The distance between two solutions is measured by their relative entropy, which to our knowledge was never used before in stability estimates. The logarithm of the strong solution is required to have polynomial growth while the weak solution can be any H-solution with sufficiently many moments at initial time. Since we require a substantial amount of regularity on the strong solution, we also provide an example of sufficient conditions on the initial data that ensure this regularity in the Coulomb (and very soft potentials) case.

math.AP↗

arXiv2024

Strichartz estimates for geophysical fluid equations using Fourier restriction theory

We prove Strichartz estimates for the semigroups associated to stratified and/or rotating inviscid geophysical fluids using Fourier restriction theory. We prove new results for rotating stratified fluids, and recover results from [16] for rotation only, and from [17] for stratification only. Our restriction estimates are obtained by the slicing method [20], which relies on the well-known Tomas-Stein theorem for 2-dimensional spheres. To our knowledge, such a method has never been used in this setting. Moreover, when the fluid is stratified, our approach yields sharp estimates, showing that the slicing method captures all the available curvature of the surfaces of interest.

math.AP↗

arXiv2021

A remark on restriction theorems and their application to Strichartz estimates

We present an elementary approach to prove restriction theorems for particular surfaces for which the Tomas-Stein theorem does not apply, which in turn provide short proofs for well-known Strichartz estimates for associated PDEs. The method consists in applying simple restriction theorems to the level sets of the surfaces studied (for instance, spheres in the case of the cone) and then integrating the inequalities over all level sets. This allows for a different proof of sharp estimates for the wave equation, and of some estimates related to the Euler equations in the rotational framework.

math.AP↗