Our focus is the Boltzmann equation in a torus under very soft potentials around equilibrium. We analyze the asymptotics of the equation from angular cutoff to non-cutoff. We first prove a refined decay result of the semi-group stemming from the linearized Boltzmann operator. Then we prove the global well-posedness of the equations near equilibrium, refined decay patterns of the solutions. Finally, we rigorously give the asymptotic formula between the solutions to cutoff and noncutoff equations with an explicit convergence rate.

中文翻译：

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从角截止到非截止的非常软势的玻尔兹曼方程的渐近分析

我们的重点是在平衡附近非常软的电势下的圆环中的玻耳兹曼方程。我们分析了从角截止到非截止的方程的渐近性。我们首先证明了线性化Boltzmann算子对半群的精确衰减结果。然后，我们证明了方程在平衡附近的整体适定性，解的精细衰减模式。最后，我们以明确的收敛速度严格给出了截止和非截止方程解的渐近公式。