Classification of invariant solutions of the Boltzmann equation

Yu N Grigoryev, S V Meleshko, P Sattayatham
1999 Journal of Physics A: Mathematical and General  
An isomorphism of the Lie algebras L 11 admissible by the full Boltzmann kinetic equation with an arbitrary differential cross section and by the Euler gas dynamics system of equations with a general state equation is set up. The similarity is also proved between extended algebras L 12 admissible by the same equations for specified power-like intermolecular potentials and for polytropic gas. This allows the solution of the problem of classification of the full Boltzmann equation invariant
more » ... ion invariant H-solutions using an optimal system of subalgebras known for the Euler system. Representations of essentially different H-solutions of the spatially inhomogeneous Boltzmann equation with one and two independent invariant variables in the explicit form are obtained on this basis.
doi:10.1088/0305-4470/32/28/102 fatcat:547j4rl2ybemtaldxooe42ldfm