The Landau-Coulomb $L^\infty$ growth conjecture

Let $f:[0,T]\times\mathbb R^3\to[0,\infty)$ be a classical solution of the space-homogeneous Landau equation with the Landau-Coulomb operator $Q$, and let $f(0,v)=f_0(v)$. The Landau-Coulomb $L^\infty$ growth conjecture. For every $(t,v)\in[0,T]\times\mathbb R^3$,

$$f(t,v)\leq\sqrt{\frac{250}{9\pi}}\max f_0(v).$$

This conjecture asserts that the $L^\infty$ norm can grow by at most the sharp dimension-three constant suggested by comparison with the asymptotic Maxwellian. Its resolution would give a uniform pointwise bound for classical solutions, but no proof or disproof is supplied here.