Generic regularity of conservative solutions to a nonlinear wave equation

The paper is concerned with conservative solutions to the nonlinear wave equation utt−c(u)(c(u)ux)x=0. For an open dense set of C3 initial data, we prove that the solution is piecewise smooth in the t-x plane, while the gradient ux 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.