1.Background and 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.

 

2.Outline and Speakers：

Instructor: Kung-Chien Wu

(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

(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)]

 

3.Time and place：

Venue: week 1 to week 11 live streaming at NCKU (Broadcasting at R. 519, Astro-Math. Bldg., NTU); week 12 to week 18 live streaming at R. 440, Astro-Math. Bldg., NTU (Broadcasting in NCKU)