Long-Time Behavior and Higher-Order Estimates in Dissipative Equations: Overview and Related Problems.

par Cilon Perusato (ICJ - Lyon 1)

mardi 19 nov. 2024, 15:45 → 16:30 Europe/Paris

Fokko (ICJ)

 In this talk we will prove results concerning upper and lower decay estimates for homogeneous Sobolev norms of solutions to a rather general family of diffusive equations. We use eventual regularity of solutions to directly work with smooth solutions in physical space, bootstrapping decay estimates from the L2 norm to higher order derivatives. Besides obtaining upper and lower bounds through this method, we also obtain reverse results: from higher order derivatives decay estimates, we deduce bounds for the L2 norm. We use these general results to prove new decay estimates for some equations and to recover some well known results. Other related results are also discussed.