Dominic Wynter
Published 2023-05-12Version 1
We prove quantitative growth estimates for large data solutions to the Boltzmann equation in one spatial dimension, for a collision kernel with angular cutoff. We prove in full the results presented in the note of Biryuk, Craig, and Panferov, and obtain improved bounds for large data. We show that solutions are unique, and propagate $W^{k,1}_\ell$ norms by a Beale-Kato-Majda criterion. We obtain quantitative uniform bounds on the density $\rho$ by $Ce^{C\sqrt{t}}$ for initial data with small relative entropy, and by $Ce^{Ct}$ for general initial data.
On the convergence from Boltzmann to Navier-Stokes-Fourier for general initial data
Low-Mach-number Euler equations with solid-wall boundary condition and general initial data
Anelastic Approximation of the Gross-Pitaevskii equation for General Initial Data
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