AMSC 698L Lecture Notes, Fall 2012

As they become available, you may download class notes here. They are pdf files.
They might be updated during the term. Please monitor the version dates.

Part I. Maxwell-Boltzmann Theory

Rarefied Gases and the Boltzmann Equation (10 September version)
Maxwell's Recipe for the Collision Operator (not available yet)
Properties of the Boltzmann Equation (10 September version)
Relation to Euler and Navier-Stokes Systems (not available yet)
Linearized Collision Operator (not available yet)
Boundary Conditions (10 September version)

Part II. Other Kinetic Theories

Classical Kinetic Theories (not available yet)
General Kinetic Theories (not available yet)
General Euler and Navier-Stokes Systems (not available yet)
Linear and Linearized Kinetic Theories (not available yet)
Analytic Methods for Linear Kinetic Theories (not available yet)

Part III. Fluid Dynamical Approximations

Hilbert and Chapman-Enskog Expansions (not available yet)
Initial and Boundary Layers (not available yet)
Beyond Navier-Stokes (not available yet)
Linear and Weakly Nonlinear Fluid Systems (not available yet)
More Fluid Systems (not available yet)

IV. Global Solutions for Fluid Systems

Linear Fluid Systems (not available yet)
Leray Theory for Incompressible Navier-Stokes (not available yet)

IV. Global Solutions for Boltzmann Equations

Solutions for Linear Cases (not available yet)
Kaniel-Shinbrot Theory (not available yet)
Control from Entropy and Dissipation Bounds (not available yet)
Velocity Averaging (not available yet)
DiPerna-Lions Theory (not available yet)

IV. Global Solutions for Boltzmann Equations

Limits for Linear Cases (not available yet)
Control of Fluctuations (not available yet)
Limits to Linear Fluid Systems (not available yet)
An Incompressible Navier-Stokes Limit (not available yet)
An Incompressible Euler Limit (not available yet)