Series Title
" From Boltzmann Equations to Gas Dynamics "
Abstract

Lecture 1 (download)
Introduction to the Boltzmann Equation
Monday, Mar 5, 4-5 PM, MS 5148

Lecture 2 (download)
Gas Dynamical Approximations
Wednesday, Mar 7, 4-5 PM, MS 5217

Lecture 3 (download)
From DiPerna-Lions to Leray
Friday, Mar 9, 4-5 PM, MS 5148

References and Background Reading:

The primary reference for these lectures will be the article based on a six-lecture short course:

1) F. Golse and C.D. Levermore,
"Hydrodynamic Limits of Kinetic Models",
Fields Institute Communications, Volume 46 (2005), 1-75.

The following secondary references cover key topics in more depth. Of these, references 2, 3, 6, 7, and 8 may be most helpful.
The DiPerna-Lions theory that provides the setting for much recent work:

2) R.J. DiPerna and P.L. Lions,
"On the Cauchy Problem for the Boltzmann Equation:
Global Existence and Weak Stability Results",
Annals of Math., Volume 130 (1990), 321-366.

The program to connect DiPerna-Lions solutions to fluid dynamics was initiated in:

3) C. Bardos, F. Golse, and C.D. Levermore
"Fluid Dynamic Limits of the Boltzmann Equation",
J. Stat. Phys., Volume 63 (1991), 323-344.

The first result that established local conservation laws:

4) C. Bardos, F. Golse, and C.D. Levermore
"The Acoustic Limit for the Boltzmann Equation",
Arch. Rational Mech. and Anal., Volume 153 (2000), 177-204.

The first results to control the acoustic waves in a nonlinear limit.

5) P.L. Lions and N. Masmoudi,
"From Boltzmann Equation to the Incompressible Navier-Stokes
and Euler Equations I and II",
Arch. Rational Mech. and Anal., Volume 158 (2001),
173-193, 195-211.

An improved treatment of local conservation laws and the first result that controlled heat fluxes:

6) F. Golse and C.D. Levermore,
"The Stokes-Fourier and Acoustic Limits
or the Boltzmann Equation"
Commun. on Pure and Appl. Math., Volume 55 (2002)

The Golse-Saint Raymond theorem connecting DiPerna-Lions solutions
of the Boltzmann equation to Leray solutions of the incompressible
Navier-Stokes motion equation:

7) F. Golse and L. Saint-Raymond,
"The Navier-Stokes Limit of the Boltzmann Equation
for Bounded Collision Kernels",
Invent. Math., Volume 155 (2004), 81-161.

The key new reguality tool that they developed is in a beautiful note:

8) F. Golse and L. Saint-Raymond,
"Velocity Averaging in L^1 for the Transport Equation"
C.R. Acad. Sci., Volume 334 (2002), 557-562.