论文标题
玻尔兹曼方程的自我生成的下限和延续
Self-generating lower bounds and continuation for the Boltzmann equation
论文作者
论文摘要
对于在整个空间中构成的空间不均匀的非切割Boltzmann方程$ \ Mathbb r^3_x $，我们建立了即使在最初的数据中包含真空区域即使是即时出现的下降下限。我们的下限仅取决于溶液的质量和能量密度的初始数据和上限。作为一种应用，我们通过删除下面有界限的质量和熵的假设来改善大数据溶液的最弱延续标准。
For the spatially inhomogeneous, non-cutoff Boltzmann equation posed in the whole space $\mathbb R^3_x$, 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.
