Kinetic equations and related topics
Tue. 15:10~17:00 and Thu. 11:10~12:00, September 11, 2018 - January 8, 2019
Instructor: Kung-Chien Wu (NCKU)
(a) Course Outline: brief introduction to kinetic theory, linearized collision operator, quantitative pointwise estimate of the linearized Boltzmann equation in hard sphere, regularization estimate.
(b) Prerequisite Course(s): Real analysis and PDE
(c) Grading: Student presentation
(d) Textbook: T.P. Liu and S.H. Yu, Solving Boltzmann equation, Part I : Green's function, Bull. Inst. Math. Acad. Sin. (N.S.), 6(2011), 151-243.
Instructor: Kazuo Aoki (NCKU/NCTS)
(a) Course Outline: boundary conditions for the Boltzmann equation, non-dimensionalization
and similarity laws, Chapman-Enskog and Hilbert expansions and fluid-dynamic equations, slip boundary conditions for the compressible Navier-Stokes equations.
(b) Prerequisite Course(s): Linear algebra and multi-variable calculus.
(c) Grading: Student presentation
(c) Textbook: None. [Reference: Y. Sone, Kinetic Theory and Fluid Dynamics (Birkhauser, 2002); Molecular Gas Dynamics: Theory, Techniques, and Applications (Birkhauser, 2007)]
Background & Purpose：
The main purposes of this course are
(1) to construct the quantitative pointwise estimate of the linearized Boltzmann equation with hard sphere case and
(2) to give an understanding of the relation between the Boltzmann equation and the fluid-dynamic equations including their boundary conditions.
This is an advanced course that conducts research ideas and technical machinery for the investigation of Boltzmann equations. We aim to prepare graduate students for the research of the Boltzmann equations.