Abstract: In 1998 it was shown by Villani that weak solutions to the spatially homogeneous Landau and Boltzmann equations that model rarefied gases with very strong repulsive intermolecular forces can exist under the a priori assumption that the rate of entropy decay (a.k.a. entropy dissipation rate) is finite for all time t >0. Since then, all existence, regularity, long time behavior results about the Landau and Boltzmann equations in this case have assumed finite rate of entropy decay. In this talk we will discuss if it is possible to replace this entropy condition by extra conditions on the initial data only.