Formation of shocks for quasilinear wave equations

Formation of shocks for quasilinear wave equations

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Yu Pin , Tsinghua University
Fine Hall 314

For any nonzero real constant $c_0$, we exhibit a family of smooth initial data for $$\big(-1 + c_0 (\partial_t \varphi)^2\big)\partial_t^2 \varphi + \triangle \varphi = 0 $$ and show that shocks form in the future. No symmetry condition is assumed. The work combines ideas from fluid mechanics, e.g. shock formation for Euler equations, and from general relativity, e.g. nonlinear stability of Minkowski spacetime and formation of trapped surfaces. This is joint with S. Miao.