LORENTZ SPACES IN ACTION ON PRESSURELESS SYSTEMS ARISING FROM MODELS OF COLLECTIVE BEHAVIOR RAPHAËL DANCHIN AND PIOTR BOGUS LAW MUCHA

Raphaël Danchin (1) , Piotr Bogusław Mucha (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 Instytut Matematyki Stosowanej i Mechaniki

We are concerned with global-in-time and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior (like traffic, crowds or birds). The initial data are rough: in particular, the density is only bounded. Our results are based on interpolation and parabolic maximal regularity, where Lorentz spaces play a key role.

Domaines: Equations aux dérivées partielles [math.AP]

Raphaël Danchin, Piotr Bogusław Mucha. LORENTZ SPACES IN ACTION ON PRESSURELESS SYSTEMS ARISING FROM MODELS OF COLLECTIVE BEHAVIOR RAPHAËL DANCHIN AND PIOTR BOGUS LAW MUCHA. 2020. ⟨hal-02568285v1⟩