Incompressible Navier-Stokes limit of non-bilinear kinetic equations and application to the BGK, nonlinear Fokker-Planck and Boltzmann-Fermi-Dirac equations

2026/07/21 by Pierre Gervais · 1 citation
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Abstract

We consider collisional kinetic equations whose collision operator is not necessarily bilinear and prove quantitative convergence to the Navier-Stokes-Fourier system in weighted Sobolev spaces, together with a description of the initial layers. The aim of this paper is to conciliate the conditional convergence result of Bardos-Golse-Levermore for abstract kinetic equations conserving macroscopic quantities and dissipating entropy with the spectral strategy initiated by Bardos-Ukai for the Boltzmann equation. This work extends the abstract approach of Gervais-Lods which was restricted to bilinear collisions (Boltzmann, Landau or quadratic approximation of other models) to non-bilinear models such as the Boltzmann-Fermi-Dirac equation, the BGK equation and the nonlinear Fokker-Planck equation.

Citations

• Fluid dynamic limits of kinetic equations. I. Formal derivations

Cited by

• Incompressible Navier-Stokes-Fourier limit from a nonlinear quantum Fokker-Planck equation

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