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Hydrodynamic Alignment with Pressure

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FKTW03 - Frontiers in kinetic equations for plasmas and collective behaviour

We study the hydrodynamic description which   arises from agent-based dynamics driven by velocity alignment.   It is known that in the pressure-less case, the Euler alignment system admits a limiting ``flocking’’ velocity, provided the solutions remain globally smooth. Here we extend the discussion, to include alignment dynamics driven by general pressure law, beyond the mono-kinetic closure.    Specifically, we address general kinetic-based mesoscopic descriptions, proving that despite the lack of closure of the pressure term,  alignment drives smooth solution to flock.

This talk is part of the Isaac Newton Institute Seminar Series series.

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