The Initial Boundary Value Problem for the Boltzmann Equation with Soft Potential
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题目: The Initial Boundary Value Problem for the Boltzmann Equation with Soft Potential
摘要: Boundary effects are central to the dynamics of the dilute particles governed by the Boltzmann equation. In this talk, I will present the existence and the large time behavior for the solutions of the initial-boundary value problem of the Boltzmann equation with soft potentials, in which the collision kernel is ruled by the inverse power law. We ﬁrst discuss the L2 argument and its interplay with intricate L∞ analysis for the linearized Boltzmann equation. Based on it, we establish the global existence and then obtain the exponential decay in L∞ space for the nonlinear Boltzmann equation. A new time-velocity weighted L∞ theory has been developed to overcome the difficulties from the zero lower bound of the collision frequency and the singularity of the collision kernel. This is a joint work with S.Q. Liu.