Well-posedness of a one-dimensional variational wave system with far field degeneracy

Rumeng Huang; Jianjun Chen; Yanbo Hu; Rumeng Huang; Jianjun Chen; Yanbo Hu

doi:10.3934/era.2026330

Electronic Research Archive

2026, Volume 34, Issue 10: 7651-7677. doi: 10.3934/era.2026330

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Research article

Well-posedness of a one-dimensional variational wave system with far field degeneracy

Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, China

Received: 15 June 2026 Revised: 11 August 2026 Accepted: 21 August 2026 Published: 07 September 2026

This work studied the local well-posedness of the Cauchy problem for a one-dimensional variational wave system arising from the theory of nematic liquid crystals. The system is degenerate and singular at spatial infinity. We applied the method of characteristics and the contraction mapping principle to establish the local existence and uniqueness of classical solutions. A suitable weighted $ L^\infty $ norm was introduced to ensure that the solution has no loss of regularity and the existence time of the solution is independent of the spatial variable.
- variational wave system,
- far field degeneracy,
- well-posedness,
- weighted $ L^\infty $ norm
Citation: Rumeng Huang, Jianjun Chen, Yanbo Hu. Well-posedness of a one-dimensional variational wave system with far field degeneracy[J]. Electronic Research Archive, 2026, 34(10): 7651-7677. doi: 10.3934/era.2026330

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Abstract

This work studied the local well-posedness of the Cauchy problem for a one-dimensional variational wave system arising from the theory of nematic liquid crystals. The system is degenerate and singular at spatial infinity. We applied the method of characteristics and the contraction mapping principle to establish the local existence and uniqueness of classical solutions. A suitable weighted $ L^\infty $ norm was introduced to ensure that the solution has no loss of regularity and the existence time of the solution is independent of the spatial variable.

References

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