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arXiv · 2002.05355

Modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition

Dongxiao Yu
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Abstract

We prove the existence of the modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition. This is accomplished in three steps. First, we derive a new reduced asymptotic system for the quasilinear wave equation by modifying H\"{o}rmander's method. Next, we construct an approximate solution, by solving our new reduced system given some scattering data at infinite time. Finally, we prove that the quasilinear wave equation has a global solution which agrees with the approximate solution at infinite time.

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Dongxiao Yu. 2020-02-13. Modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition. https://doi.org/10.1007/s00220-021-03989-0

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