Self-generating lower bounds and continuation for the Boltzmann equation
Self-generating lower bounds and continuation for the Boltzmann equation
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DOI：
10.1007/s00526-020-01856-9
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发表时间：
2020-05
影响因子：
2.1
通讯作者：
Christopher Henderson;Stanley Snelson;Andrei Tarfulea
中科院分区：
文献类型：
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作者：
Christopher Henderson;Stanley Snelson;Andrei Tarfulea
对于在整个空间中提出的空间非齐次、无截断的Boltzmann方程，我们建立了在初始数据包含真空区的情况下瞬时出现的逐点下界。我们的下界仅取决于解的质量密度和能量密度的初始数据和上界。作为应用，我们改进了大数据解的已知最弱连续性准则，去掉了质量在下有界和熵在上有界的假设。
For the spatially inhomogeneous, non-cutoff Boltzmann equation posed in the whole space, we establish pointwise lower bounds that appear instantaneously even if the initial data contains vacuum regions. Our lower bounds depend only on the initial data and upper bounds for the mass and energy densities of the solution. As an application, we improve the weakest known continuation criterion for large-data solutions, by removing the assumptions of mass bounded below and entropy bounded above.