The paper is concerned with conservative solutions to the nonlinear wave equation . For an open dense set of initial data, we prove that the solution is piecewise smooth in the t–x plane, while the gradient can blow up along finitely many characteristic curves. The analysis is based on a variable transformation introduced in , which reduces the equation to a semilinear system with smooth coefficients, followed by an application of Thom's transversality theorem.
Cite this article
Alberto Bressan, Geng Chen, Generic regularity of conservative solutions to a nonlinear wave equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 2, pp. 335–354DOI 10.1016/J.ANIHPC.2015.12.004