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

  • * Corresponding author: Jie Ji

    * Corresponding author: Jie Ji 
This work is supported by NSFC under Grant NO.11771236
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  • 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.

    Mathematics Subject Classification: Primary: 35Q20; Secondary: 35B65.


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