On the Global Existence of Weak Solutions to A Nonlinear Variational Wave Equation

Ping Zhang; Yuxi Zheng

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Weak solutions to a nonlinear variational wave equation with general data

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In this paper we present some results on the global existence of weak solutions to a nonlinear variational wave equation and some related problems. We first introduce the main tools, the $L^{p}$ Young measure theory and related compactness results, in the first section. Then we use the $L^{p}$ Young measure theory to prove the global existence of dissipative weak solutions to the asymptotic equation of the nonlinear wave equation, and comment on its relation to Camassa-Holm equations in the second...

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