FINITENESS OF ENTROPY FOR GRANULAR MEDIA EQUATIONS
Abstract: The current work deals with the granular media equation whose probabilistic
interpretation is the McKean–Vlasov diffusion. It is well known that the Laplacian provides a
regularization of the solution. Indeed, for any , the solution is absolutely continuous
with respect to the Lebesgue measure. It has also been proved that all the moments are
bounded for positive . However, the finiteness of the entropy of the solution is a new result
which will be presented here.
2000 AMS Mathematics Subject Classification: Primary: 35K55; Secondary: 60J60,
60E15.
Keywords and phrases: Granular media equation, McKean–Vlasov diffusion,
Wasserstein distance, functional inequalities, entropy.