## Blowup of small data solutions for a quasilinear wave equation in two space dimensions.(English)Zbl 1080.35043

Summary: For the quasilinear wave equation $$\partial_t^2u - \Delta u = u_t u_{tt},$$ we analyze the long-time behavior of classical solutions with small (not rotationally invariant) data. We give a complete asymptotic expansion of the lifespan and describe the solution close to the blow-up point. It turns out that this solution is a “blow-up solution of cusp type,” according to the terminology of the author.

### MSC:

 35L70 Second-order nonlinear hyperbolic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs

### Keywords:

Cauchy problem; Hörmander’s conjecture
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