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Shuangrong Li, Yanbo Hu, Conservative weak solutions to a radially symmetric variational wave system outside a ball

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DOI: 10.23952/jnva.10.2026.5.01

Volume 10, Issue 5, 1 October 2026, Pages 867-894

 

Abstract. We study the initial-boundary value problem for a radially symmetric variational wave system arising from the theory of nematic liquid crystals. Based on the characteristic reflection method, we introduce the energy-dependent coordinates into the semi-infinite interval to transform the original problem into a new boundary value problem. By regularizing the governing system and deriving the a priori estimates of solutions, we apply the Young measure theory to show the strong convergence of the approximate solution sequence and then establish the global existence of weak solutions for the new boundary value problem. The global conservative weak solution of the original initial-boundary value problem is constructed by returning the solution in terms of energy-dependent coordinate variables to the physical plane.

 

How to Cite this Article:
S. Li, Y. Hu, Conservative weak solutions to a radially symmetric variational wave system outside a ball, J. Nonlinear Var. Anal. 10 (2026), 867-894.