Abstract
This work deals with the non-cutoff Boltzmann equation for all types of potentials, in both the torus \mathbf{T}^{3} and in the whole space \mathbf{R}^{3} , 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.
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