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    Generic Regularity of Conservative Solutions to a Nonlinear Wave Equation

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    The paper is concerned with conservative solutions to the nonlinear wave equation uttβˆ’c(u)(c(u)ux)x=0u_{tt} - c(u)\big(c(u) u_x\big)_x = 0. For an open dense set of C3C^3 initial data, we prove that the solution is piecewise smooth in the tt-xx plane, while the gradient uxu_x can blow up along finitely many characteristic curves. The analysis is based on a variable transformation introduced in [7], which reduces the equation to a semilinear system with smooth coefficients, followed by an application of Thom's transversality theorem.Comment: 25 page
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