Hydrodynamic limit for the non-cutoff Boltzmann equation

  • Chuqi Cao

    The Hong Kong Polytechnic University, Hong Kong, P. R. China
  • Kleber Carrapatoso

    Institut Polytechnique de Paris, Palaiseau, France
Hydrodynamic limit for the non-cutoff Boltzmann equation cover

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Abstract

This work deals with the non-cutoff Boltzmann equation for all types of potentials, in both the torus and in the whole space , under the incompressible Navier–Stokes scaling. We first establish the well-posedness and decay of global mild solutions to this rescaled Boltzmann equation in a perturbative framework, that is, for solutions close to the Maxwellian, obtaining in particular integrated-in-time regularization estimates. We then combine these estimates with spectral-type estimates in order to obtain the strong convergence of solutions to the non-cutoff Boltzmann equation towards the incompressible Navier–Stokes–Fourier system.

Cite this article

Chuqi Cao, Kleber Carrapatoso, Hydrodynamic limit for the non-cutoff Boltzmann equation. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024), published online first

DOI 10.4171/AIHPC/139