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Are there more than five linearly-independent collision invariants for the Boltzmann equation? (English) Zbl 0718.60113
Summary: The problem of finding the summational collision invariants for the Boltzmann equation is tackled with the aim of proving that the most general solution of the problem is not different from the standard one even when the equation defining a collision invariant \(\psi\) is only satisfied almost everywhere in \(R^3\times R^3\times S^2\). The collision invariant \(\psi\) is assumed to be in the Hilbert space \(H_{\omega}\) of the functions which are square integrable with respect to a Maxwellian weight.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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