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Blair, M.D., Smith, H.F. and Sogge, C.D. (2009) Strichartz Estimates for the Wave Equation on Manifolds with Boundary. Annales de l’Institut Henri Poincaré C, Analyse non linéaire, 26, 1817-1829.
https://doi.org/10.1016/j.anihpc.2008.12.004

has been cited by the following article:

• 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