Shock Profile Solutions of the Boltzmann Equation*
نویسنده
چکیده
Shock waves in gas dynamics can be described by the Euler Nav ie r 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 Navie r 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 c o and the shock speed s.
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