TITLE:
Well-Posedness for Quintic Energy Critical Wave in 3D Cylindrical Convex Domains
AUTHORS:
Len Meas
KEYWORDS:
Energy Critical Waves, Cylindrical Domains, Dispersive Estimates, Strichartz Estimates
JOURNAL NAME:
Open Access Library Journal,
Vol.13 No.4,
April
2,
2026
ABSTRACT: In this work, we prove that the quintic energy critical wave inside a cylindrical convex domain
Ω⊂
ℝ
3
with smooth boundary
∂Ω≠∅
is well-posed in energy space. The dispersive estimates found in [1] and the Strichartz estimates found in [2] are essential resources for demonstrating local well-posedness. We note that our findings on the local and global existence of the wave equation solution in the cylindrical domain setting interpolate between those in any bounded domains in
ℝ
3
and in Euclidean space
ℝ
3
. Furthermore, when combined with the trace estimates and the nonconcentration of nonlinear effect in a small light cone, the result of the Strichartz estimates in our context is strong enough to allow us to extend local to global well-posedness. Subject AreasPartial Differential Equations