On a novel gradient flow structure for the aggregation equation

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

The aggregation equation arises naturally in kinetic theory in the study of granular media, and its interpretation as a 2-Wasserstein gradient flow for the nonlocal interaction energy is well-known. Starting from the spatially homogeneous inelastic Boltzmann equation, a formal Taylor expansion reveals a link between this equation and the aggregation equation with an appropriately chosen interaction potential. Inspired by this formal link and the fact that the associated aggregation equation also dissipates the kinetic energy, we present a novel way of interpreting the aggregation equation as a gradient flow, in the sense of curves of maximal slope, of the kinetic energy, rather than the usual interaction energy, with respect to an appropriately constructed transportation metric on the space of probability measures.

Details

OriginalspracheEnglisch
Aufsatznummer126
FachzeitschriftCalculus of variations and partial differential equations
Jahrgang63
Ausgabenummer5
PublikationsstatusVeröffentlicht - Juni 2024
Peer-Review-StatusJa

Schlagworte

ASJC Scopus Sachgebiete

Schlagwörter

  • 35A01, 35A15, 35Q20, 35Q70, 82C22