Abstract
Shock waves in gas dynamics can be described by the Euler Navier-Stokes, or Boltzmann equations. We prove the existence of shock profile solutions of the Boltzmann equation for shocks which are weak. The shock is written as a truncated expansion in powers of the shock strength, the first two terms of which come exactly from the Taylor tanh (x) profile for the Navier-Stokes solution. The full solution is found by a projection method like the Lyapunov-Schmidt method as a bifurcation from the constant state in which the bifurcation parameter is the difference between the speed of sound c0 and the shock speed s.
Original language | English (US) |
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Pages (from-to) | 161-194 |
Number of pages | 34 |
Journal | Communications In Mathematical Physics |
Volume | 86 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1982 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics