Generalized solutions for inextensible string equations

2014/01/13 by Yasemin Şengül, Dmitry Vorotnikov, Şengül, Yasemin +1
Engineering · Mathematics · Physics and Astronomy · #35D99 #35L99 #35Q74 #74H20 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.1401.2717

openalex publication_date 2014/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the system of equations of motion for inextensible strings. This system possesses many internal symmetries, and is related to discontinuous systems of conservation laws and the total variation wave equation. We prove existence of generalized Young measure solutions with non-negative tension after transforming the problem into a system of conservation laws and approximating it with a regularized system for which we obtain uniform estimates of the energy and the tension. We also discuss sufficient conditions for non-negativity of the tension for strong solutions.

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