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Online ISSN 1552-4485; Print ISSN 0033-569X
On the analyticity of the flow map for the AHT equations
Authors:
Amina Mecherbet and Franck Sueur
Journal:
Quart. Appl. Math.
MSC (2020):
Primary 35A20, 35Q49; Secondary 49Q22
DOI:
https://doi.org/10.1090/qam/1713
Published electronically:
April 23, 2025
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Abstract | References | Similar Articles | Additional Information
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.
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Additional Information
Amina Mecherbet
Affiliation:
Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Paris Cité, 8 Place Aurélie Nemours, F75205 Paris Cedex 13, France
MR Author ID:
1346375
Email:
mecherbet@imj-prg.fr
Franck Sueur
Affiliation:
Department of Mathematics, Maison du nombre, 6 avenue de la Fonte, University of Luxembourg, L-4364 Esch-sur-Alzette, Luxembourg
MR Author ID:
767819
Email:
Franck.Sueur@uni.lu
Keywords:
Analyticity in context of PDEs,
nonlinear nonlocal transport equations,
Optimal transportation
Received by editor(s):
December 22, 2024
Received by editor(s) in revised form:
March 14, 2025
Published electronically:
April 23, 2025
Additional Notes:
Both authors were partially supported by the Agence Nationale de la Recherche, Project SUSPENSIONS, grant ANR-24-CE92-0028-01. The second author was partially supported by the Agence Nationale de la Recherche, Project BOURGEONS, grant ANR-23-CE40-0014-01.
Article copyright:
© Copyright 2025
Brown University