Geodesic
Generic regularity of conservative solutions to a nonlinear wave equation
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 2, pp. 335-354
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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.

DOI : 10.1016/j.anihpc.2015.12.004
Keywords: Nonlinear wave equations, Generic regularity, Singularity 
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     author = {Bressan, Alberto and Chen, Geng},
     title = {Generic regularity of conservative solutions to a nonlinear wave equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {335--354},
     year = {2017},
     publisher = {Elsevier},
     volume = {34},
     number = {2},
     doi = {10.1016/j.anihpc.2015.12.004},
     mrnumber = {3610935},
     zbl = {1375.35062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.12.004/}
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Bressan, Alberto; Chen, Geng. Generic regularity of conservative solutions to a nonlinear wave equation. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 2, pp. 335-354. doi: 10.1016/j.anihpc.2015.12.004

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