= Local Maxwellian
{title2=$\mathcal M(t,x,v)=\exp(a(t,x)+b(t,x)\cdot v+c(t,x)|v|^2),\quad c<0$}
= Maxwellian
{c}
{synonym}
A Gaussian velocity profile at each position, with coefficients encoding local density, mean velocity and temperature. Its logarithm is a <linear combination> of <collision invariants>, so its collision term vanishes pointwise in position. Transport need not vanish: the coefficients must also satisfy their transport equations for a <local Maxwellian> to solve the full <Boltzmann equation>.
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