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Generic Regularity of Conservative Solutions to a Nonlinear Wave Equation
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
- plane, while the gradient 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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