On a novel gradient flow structure for the aggregation equation

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Contributors

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

Original languageEnglish
Article number126
JournalCalculus of variations and partial differential equations
Volume63
Issue number5
Publication statusPublished - Jun 2024
Peer-reviewedYes

Keywords

ASJC Scopus subject areas

Keywords

  • 35A01, 35A15, 35Q20, 35Q70, 82C22

Library keywords