5 research outputs found
Instabilities in the mean field limit
Consider a system of particles interacting through Newton's second law
with Coulomb interaction potential in one spatial dimension or a
smooth potential in any dimension. We prove that in the mean
field limit , the particles system displays instabilities
in times of order for some configurations approximately distributed
according to unstable homogeneous equilibria.Comment: minor typos corrected; Journal of Statistical Physics, accepte
Ill-posedness of the hydrostatic Euler and singular Vlasov equations
In this paper, we develop an abstract framework to establish ill-posedness in
the sense of Hadamard for some nonlocal PDEs displaying unbounded unstable
spectra. We apply it to prove the ill-posedness for the hydrostatic Euler
equations as well as for the kinetic incompressible Euler equations and the
Vlasov-Dirac-Benney system