Work

On the analyticity of the flow map for the AHT equations

Year: 2025

Type: article

Abstract: The AHT equation is a nonlinear and nonlocal vectorial transport equation which was introduced by Angenent, Haker, and Tannenbaum [SIAM J. Math. Anal. 35 (2003), pp. 61–97] in optimal transport theory. For this equation, classical solutions are known to exist at least locally in time, and a flow map can thus be uniquely associated with these solutions. In this paper we consider the case where the equation is set in a bounded domain with an analytic boundary and we prove that the flow map is analytic with respect to time.

Source: Quarterly of Applied Mathematics

DOI: 10.1090/qam/1713

Authors: Amina Mecherbet, Franck Sueur

Institutions: Université Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, University of Luxembourg

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: Boundaries, Congestion and Vorticity in Fluids: A connection with environmental issues, G6268741103, Derivation and analysis of effective suspension models