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arXiv · 1502.02611

Generic Regularity of Conservative Solutions to a Nonlinear Wave Equation

Alberto Bressan·Geng Chen
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Abstract

The paper is concerned with conservative solutions to the nonlinear wave equation $u_{tt} - c(u)\big(c(u) u_x\big)_x = 0$. For an open dense set of $C^3$ initial data, we prove that the solution is piecewise smooth in the $t$-$x$ plane, while the gradient $u_x$ 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.

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Alberto Bressan, Geng Chen. 2015-02-09. Generic Regularity of Conservative Solutions to a Nonlinear Wave Equation. https://arxiv.org/abs/1502.02611

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