Well-Posedness for Quintic Energy Critical Wave in 3D Cylindrical Convex Domains

In this work, we prove that the quintic energy critical wave inside a cylindrical convex domain $\Omega \subset {ℝ}^3$ with smooth boundary $\partial \Omega \ne \varnothing$ 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.