Non Maxwellian long-time asymptotics for Homoenergetic Boltzmann flows under strong shear

Abstract

We compute, using matched asymptotic expansions, the long-time asymptotics of homoenergetic solutions to the nonlinear Boltzmann equation, in presence of a shear term, in the hyperbolic dominated regime, for homogeneous collision kernels for which there are infinitely many collisions as $τ\to \infty$. The mass of the resulting solutions is concentrated in an increasing family of dyadic scales, something that makes the behaviour of these solutions very different from classical Maxwellian distributions.