報告人：何淩冰（清華大學）

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

報告摘要：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.

報告時間：2024年8月11日（星期日）9:30-11:00

報告地點：東32樓115會議室

邀請人：雷遠傑

報告人簡介：何淩冰，教授，清華大學數學系，主要研究方向為Boltzmann方程及Landau方程解的正則性傳播和漸進性行為。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.等國際主流數學雜志發表論文30餘篇。