• Schild Mathematik Ost
Mathematische Strömungsmechanik

Seminarreihe "structure preserving numerical methods for hyperbolic equations" im Oberseminar Mathematische Strömungsmechanik

Global regularity and emergent behavior of multi-dimensional Euler alignment system
Datum: 11.03.2022, 15:00 - 16:00 Uhr
Kategorie: Seminar, Veranstaltung
Vortragende:r: Eitan Tadmor

This talk is part of the seminar series "structure preserving numerical methods for hyperbolic equations", click here for more details 


We study the hydrodynamic description of alignment dynamics. It is known that such Euler alignment systems must flock, namely, the large time behavior of the velocity field approaches a limiting “flocking” velocity, provided the solutions remain globally smooth. To address the question of global regularity, we derive a critical threshold condition in the phase space of initial configurations which guarantees global regularity. It is known that global smooth solutions exist in one and two spatial dimensions, subject to sub-critical initial data. Here, we settle the question of existence for arbitrary dimension. The proof is based on identifying a proper invariant regions.

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