2008/03/31 by Michael Kunzinger, Roman O. Popovych · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #math-ph #math.MP #msc:35A30 #msc:35A99 #msc:35K05 #msc:35K57
paper · pdf · doi:10.1063/1.2993117
published as J. Math. Phys. 49 (2008), 103506, 34 pp · 36 pages, extended version
arxiv created 2008/04/15 · openalex publication_date 2008/10/01 · arxiv updated 2010/11/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially depend on potential variables. This statement provides a significant generalization of results of the recent paper by Bluman et al. [J. Math. Phys. 47, 113505 (2006)]. Moreover, we present extensions to gauged potential systems, Abelian and general coverings, and general foliated systems of differential equations. An example illustrating possible applications of these results is given. A special version of the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are proposed as new tools for the investigation of potential conservation laws.