## EVENT DETAILS AND ABSTRACT

**PDE Seminar**
**Title:** Nonlinear Boundary Layers of the Boltzmann Equation

**Speaker:** Professor Tong Yang

**Speaker Info:** City University of Hong Kong

**Brief Description:**

**Special Note**:

**Abstract:**

This is a joint work with Seiji Ukai and
Shih-Hsien Yu. We study the half-plane problem of
the nonlinear Boltzmann equation,
assigning the Dirichlet data
for outgoing particles at the boundary
and a Maxwellian as the far field.
We will show that the solvability condition of the problem changes with
the
Mach number ${\mathscr M}^\infty$ of the far field Maxwellian.
If ${\mathscr M}^\infty<-1$,
there exists a unique smooth solution connecting the Dirichlet
data and the far field Maxwellian for any Dirichlet data sufficiently
close
to the far field Maxwellian. Otherwise, such a solution exists
only for the Dirichlet data satisfying certain admissible conditions.
The set of admissible Dirichlet data forms a smooth
manifold of co-dimension 1 for the case $-1<{\mathscr M}^\infty<0$,
4 for $0<{\mathscr M}^\infty<1$ and 5 for ${\mathscr M}^\infty>1$,
respectively. We also show that the same is true for the linearized
problem at the far field Maxwellian, and the manifold is, then, a
hyperplane.
The proof is
essentially based on the macro-micro or hydrodynamic-kinetic
decomposition of solutions combined with an artificial
damping term and a spatially
exponential decay weight.

**Date:** Thursday, May 30, 2002

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Prof. Gui-Qiang Chen

**Contact email:** gqchen@math.northwestern.edu

**Contact Phone:** 847-491-5553

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