Radjesvarane Alexandre

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We study Boltzmann's collision operator for long-range interactions, i.e. without Grad's angular cutoff assumption. We establish a functional inequality showing that the entropy dissipa-tion controls smoothness of the distribution function, in a precise sense. Our estimate is optimal, and gives a unified treatment of both the linear and the nonlinear cases.(More)
The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cross-section. However, even though so far this has been justified satisfactorily for the spatially homogeneous Boltzmann equation, it is still basically unsolved for the spatially(More)
We use Littlewood Paley decompositions and related arguments to study some regularity questions in Boltzmann equation. This is done in the framework of homogeneous solutions, with a scattering cross section of Maxwell type, without assuming the usual Grad's cutoff assumption. Although the recent results of Desvillettes and Wennberg include larger(More)
For the first time, a proof of the sifting process (SP) and so the empirical mode decomposition (EMD), is given. For doing this, lower and upper envelopes are modeled in a more convenient way that helps us prove the convergence of the SP towards a solution of a partial differential equation (PDE). We also prove that such a PDE has a unique solution, which(More)