The Boltzmann-BGK model with nontrivial collision frequency near vacuum

We study the Cauchy problem for the Boltzmann-BGK model in the three-dimensional whole space with nontrivial collision frequency $ν(f)=ρ^αT^β$, where $α\in(1/3,1]$, $β\in[0,1]$, and $3α+2β\geq 2$. Existing well-posedness results for such models have largely been confined to near-equilibrium regimes