5 papers · 1 filter
Singular mean-field limits via a multiscale mollification metric
Quoc Hung Nguyen, Sylvia Serfaty
We consider a general class of first order ODE systems for the evolution of interacting particles (in Euclidean space ) in a mean-field regime. The class of inter…
Another look at regularity in transport-commutator estimates
Elias Hess-Childs, Matthew Rosenzweig, Sylvia Serfaty
We are interested in how regular a transport velocity field must be in order to control Riesz-type commutators. Estimates for these commutators play a central role in the analysis…
A sharp commutator estimate for all Riesz modulated energies
Elias Hess-Childs, Matthew Rosenzweig, Sylvia Serfaty
We prove a functional inequality in any dimension controlling the derivative along a transport of the Riesz modulated energy in terms of the modulated energy itself. This modulated…
Sharp commutator estimates of all order for Coulomb and Riesz modulated energies
Matthew Rosenzweig, Sylvia Serfaty
We prove functional inequalities in any dimension controlling the iterated derivatives along a transport of the Coulomb or super-Coulomb Riesz modulated energy in terms of the modu…
The Lake equation as a supercritical mean-field limit
Matthew Rosenzweig, Sylvia Serfaty
We study so-called supercritical mean-field limits of systems of trapped particles moving according to Newton's second law with either Coulomb/super-Coulomb or regular interactions…