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 Global stability and scattering theory for the Boltzmann equation with soft potentials in the whole space: weak collision regime

主讲人：何凌冰

摘要：A Traveling Maxwellian $\mathcal{M} = \mathcal{M}(t, x, v)$ represents a traveling wave solution to the Boltzmann equation ? in the whole space $\R^3$(for the spatial variable $x$). The primary objective of this talk is to investigate the global-in-time stability of $\mathcal{M}$ and its associated scattering theory in ? $L^1_{x,v}$ space for the ?Boltzmann equation with soft potentials when the dissipative effects induced by collisions are {\it weak}. We demonstrate the following results: (i) $\mathcal{M}$ exhibits Lyapunov stability; (ii) The perturbed solution, which is assumed to satisfy the same conservation law as $\mathcal{M}$, scatters in the $L^1_{x,v}$ space towards a particular traveling wave (with an explicit convergence rate), which may not necessarily be $\mathcal{M}$. The key elements in the proofs involve the formulation of the {\it Strichartz-Scaled Boltzmann equation}(achieved through the Strichartz scaling applied to the original equation) and the propagation of analytic smoothness.

主讲人简介：何凌冰，教授，清华大学数学系，主要研究方向为Boltzmann方程及Landau方程解的正则性传播和渐进性行为。在Ann. Sci. éc. Norm. Supér、 Math. Ann.、 Ann. PDE、 Arch. Ration. Mech. Anal.、Comm. Math. Phys.、SIAM J. Math. Anal.、J. Funct. Anal.、 J. Stat. Phys.等国际主流数学杂志发表论文30余篇。

邀请人：雷远杰

时间：2024年8月11日（星期日）9:30-11:00

地点：东32楼115会议室