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## Instabilities in the mean field limit

Together with Daniel Han-Kwan, we recently wrote a paper, entitled “Instabilities in the mean field limit”, to be published on the Journal of Statistical Physics (see here for a preprint). I shall explain our main theorem below.

I go on with some basic concepts and classical results in fluid dynamics [numbering is in accordance with the previous notes]. Throughout this section, I consider compressible barotropic ideal fluids with the pressure law ${p = p(\rho)}$ or incompressible ideal fluids with constant density ${\rho = \rho_0}$ (and hence, the pressure is an unknown function in the incompressible case).