#### Vol. 14, No. 1, 2021

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
Singularities generated by the triple interaction of semilinear conormal waves

### Antônio Sá Barreto and Yiran Wang

Vol. 14 (2021), No. 1, 135–170
##### Abstract

We study the local propagation of conormal singularities for solutions of semilinear wave equations $\square u=P\left(y,u\right)$, where $P\left(y,u\right)$ is a polynomial of degree $N\ge 3$ in $u$ with ${C}^{\infty }\left({ℝ}_{y}^{3}\right)$ coefficients. We know from the work of Melrose and Ritter and Bony that if $u$ is conormal to three waves which intersect transversally at point $q$, then after the triple interaction $u\left(y\right)$ is a conormal distribution with respect to the three waves and the characteristic cone $\mathsc{𝒬}$ with vertex at $q$. We compute the principal symbol of $u$ at the cone and away from the hypersurfaces. We show that if ${\partial }_{u}^{3}P\left(q,u\left(q\right)\right)\ne 0$, then $u$ is an elliptic conormal distribution.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/apde

We have not been able to recognize your IP address 18.207.133.27 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.