Lower bound for the Boltzmann equation whose regularity grows tempered with time

Ling-Bing He, Jie Ji, Ling-Xuan Shao
2021 Kinetic and Related Models  
As a first step towards the general global-in-time stability for the Boltzmann equation with soft potentials, in the present work, we prove the quantitative lower bounds for the equation under the following two assumptions, which stem from the available energy estimates, i.e. (i). the hydrodynamic quantities (local mass, local energy, and local entropy density) are bounded (from below or from above) uniformly in time, (ii). the Sobolev regularity for the solution grows tempered with time. 2020
more » ... athematics Subject Classification. Primary: 35Q20; Secondary: 35B65. Pulvirenti and Wennberg [14] removed the restriction of the radial symmetry. They proved that any solution to (1.6) with finite mass, energy and entropy fulfills the Gaussian lower bound, i.e. for any fixed t 0 > 0. These lower bounds play an important role in the entropy method. We refer readers to references [6, 16] where the authors made a detailed study of the entropy production rate.
doi:10.3934/krm.2021020 fatcat:j63rervcmrcxbm4sev57rn4ami