勷勤数学•专家报告

题      目：Strong diffusive limit of the Boltzmann equation with Maxwell boundary condition

报  告  人： 周富军 教授  (邀请人：喻洪俊)

                                                华南理工大学

时      间： 9月12日  15：00-16:00

地     点：数科院东楼401

报告人简介:

          周富军，华南理工大学数学学院教授、博导。主要从事动理学方程及其流体力学极限等方面的研究。曾先后访问德国汉诺威莱布尼兹大学、美国布朗大学和香港中文大学，主持多项国家级和省部级课题。

摘      要：

           Although the weak diffusive limit from the Boltzmann equation to the incompressible Navier-Stokes-Fourier system was previously established for the Maxwell boundary condition within the framework of renormalized solutions [SaintRaymond2009] [Jiang-Masmoudi2017], the corresponding strong diffusive limit has remained open except for the special scaling $\alpha \sim \epsilon^{1/2}$ [Jiang-Masmoudi2017]. In this work, we resolve this problem by proving the strong diffusive limit for the full range of accommodation coefficients $\alpha \in [0,1] $ within the framework of strong solutions. The principal innovations of our proof include: (1) an $\epsilon$-stretching method for reduction to a single-bounce $L^\infty$ estimate; and (2) a dissipative decomposition based on a carefully constructed rotating Maxwellian to handle the challenging near-specular regime $\alpha \ll \epsilon$.

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