316 citations · 2.6k across the 149 of their papers we have counts for
9 papers · 2 filters
Critical thresholds in 1D Euler equations with nonlocal forces
José A. Carrillo, Young-Pil Choi, Eitan Tadmor +1
We study the critical thresholds for the compressible pressureless Euler equations with pairwise attractive or repulsive interaction forces and non-local alignment forces in veloci…
The Filippov characteristic flow for the aggregation equation with mildly singular potentials
José Antonio Carrillo, Francois James, Frédéric Lagoutière +1
Existence and uniqueness of global in time measure solution for the multidimensional aggregation equation is analyzed. Such a system can be written as a continuity equation with a…
A hybrid variational principle for the Keller-Segel system in
Adrien Blanchet, José A. Carrillo, David Kinderlehrer +3
We construct weak global in time solutions to the classical Keller-Segel system cell movement by chemotaxis in two dimensions when the total mass is below the well-known critical v…
Exponential Convergence Towards Stationary States for the 1D Porous Medium Equation with Fractional Pressure
J. A. Carrillo, Y. Huang, M. C. Santos +1
We analyse the asymptotic behaviour of solutions to the one dimensional fractional version of the porous medium equation introduced by Caffarelli and Vázquez, where the pressure is…
Regularity of local minimizers of the interaction energy via obstacle problems
J. A. Carrillo, M. G. Delgadino, A. Mellet
The repulsion strength at the origin for repulsive/attractive potentials determines the regularity of local minimizers of the interaction energy. In this paper, we show that if thi…
Nonlocal-interaction equations on uniformly prox-regular sets
José A. Carrillo, Dejan Slepčev, Lijiang Wu
We study the well-posedness of a class of nonlocal-interaction equations on general domains , including nonconvex ones. We show that under mild assumptions o…