Strong L1 convergence to equilibrium without entropy conditions for the spatially homogenous Boltzmann equation

• This paper deals with solutions to the Cauchy problem for the spatially homogeneous non-linear Boltzmann equation. The main result is that for the hard sphere kernel, a solution to the Boltzmann equation converges strongly in L1 to equilibrium given that the initial data f0 belongs to L1(R^3;(1+v^2)dv). This was previously known to be true with the additional assumption that f0logf0 belonged to L1(R^3). For the proof of the main theorem, new regularising effects for the gain term in the collision operator are derived, and previous results concerning uniform bounds on the time it takes for a solution to the Boltzmann equation to reach equilibrium are extended.

Publikations- och innehållstyp

vet (ämneskategori)

lic (ämneskategori)