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arXiv · 2008.10269

Global solutions in $W_k^{\zeta,p}L^\infty_TL^2_v$ for the Boltzmann equation without cutoff

Haoyu Zhang
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Abstract

The Boltzmann equation without an angular cutoff in a three-dimensional periodic domain is considered. The global-in-time existence of solutions in a function space $ W_k^{\zeta,p}L^\infty_TL^2_v $ with $p>1$ and $\zeta>3(1-\frac{1}{p})$ is established in the perturbation framework and the long-time behavior of solutions is also obtained for both hard and soft potentials. The proof is based on several norm estimates.

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Haoyu Zhang. 2020-08-24. Global solutions in $W_k^{\zeta,p}L^\infty_TL^2_v$ for the Boltzmann equation without cutoff. https://arxiv.org/abs/2008.10269

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