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<p>In this paper, we consider the global existence of a conservative weak solution to the Cauchy problem for a one-dimensional nonlinear variational wave system by the method of energy-dependent coordinates and the Young measure theory. Moreover, the construction of existence leads directly to continuous dependence of solutions on the initial data. It is worth noting that the energy of the solution is conserved in the sense of Radon measure. This wave equation is derived from a wave system modeling a class of nematic liquid crystals affected by electric field.</p>

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Existence of conservative weak solutions for a class of nonlinear variational wave systems

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Xiaoping Jing,
  • Wei Xiao

摘要

In this paper, we consider the global existence of a conservative weak solution to the Cauchy problem for a one-dimensional nonlinear variational wave system by the method of energy-dependent coordinates and the Young measure theory. Moreover, the construction of existence leads directly to continuous dependence of solutions on the initial data. It is worth noting that the energy of the solution is conserved in the sense of Radon measure. This wave equation is derived from a wave system modeling a class of nematic liquid crystals affected by electric field.