Chanillo, SagunYung, Po Lam2026-01-012026-01-010022-1236ORCID:/0000-0002-0441-3625/work/162951479https://hdl.handle.net/1885/733800039In this note, we consider the constant-mean-curvature wave equation in (1. +. 2)-dimensions. We show that it does not admit any self-similar blow-up. We also remark that the equation is locally well-posed for initial data in H3/2.S.C. and P.-L.Y. were supported by National Science Foundation grant DMS-1201474 . P.-L.Y. was also supported by a Titchmarsh Fellowship at the University Of Oxford , a junior research fellowship at St. Hilda's College , and a direct grant for research from the Chinese University of Hong Kong ( 4053120 ). S.C. wishes to thank Carlos Kenig for several enlightening conversations related to the contents of this paper.23enPublisher Copyright: © 2015 Elsevier Inc.Local well-posednessSelf-similar blow-upWave constant mean curvature equation2015-08-1510.1016/j.jfa.2015.01.02184930475250