statistical mechanics - Is the Maxwell distribution a solution of the Boltzmann equation?

I am studying about the Boltzmann Equation for non-equilibrium rarefied gases (dilute gases to be more specific): $$\frac{\partial f}{\partial t}+\pmb{v}\cdot\nabla_{\pmb{x}}f=Q(f,f)$$

My question is this: is the Maxwell distribution a solution of the equation above?

Answer

It has to be, because the Maxwell-Boltzmann distribution is the maximum entropy distribution. If your model does not allow relaxation to the Maxwell-Boltzmann distribution it is in conflict with the second law of thermodynamics.