Conservation laws for fourth order systems in four dimensions

2006/07/20 by Tobias Lamm, Lamm, Tobias, Tristan Rivière +2
Mathematics · #35 J 60 #58 E 20 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #math.AP #math.DG #msc:20 #msc:35 #msc:58 #msc:60

paper · pdf · doi:10.48550/arxiv.math/0607484

20 pages

arxiv created 2006/07/20 · openalex publication_date 2006/07/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following an approach of the second author for conformally invariant variational problems in two dimensions, we show in four dimensions the existence of a conservation law for fourth order systems, which includes both intrinsic and extrinsic biharmonic maps. With the help of this conservation law we prove the continuity of weak solutions of this system. Moreover we use the conservation law to derive the existence of a unique global weak solution of the extrinsic biharmonic map flow in the energy space.

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