%0 Journal Article
%T Well-Posedness for Quintic Energy Critical Wave in 3D Cylindrical Convex Domains
%A Len Meas
%J Open Access Library Journal
%V 13
%N 4
%P 1-16
%@ 2333-9721
%D 2026
%I Open Access Library
%R 10.4236/oalib.1115029
%X In this work, we prove that the quintic energy critical wave inside a cylindrical convex domain <math xmlns='http://www.w3.org/1998/Math/MathML'>
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   <mn>3</mn>
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</math>

 with smooth boundary <math xmlns='http://www.w3.org/1998/Math/MathML'>
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 is well-posed in energy space. The dispersive estimates found in <a href="#ref1">[1]</a> and the Strichartz estimates found in <a href="#ref2">[2]</a> 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 <math xmlns='http://www.w3.org/1998/Math/MathML'>
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 and in Euclidean space <math xmlns='http://www.w3.org/1998/Math/MathML'>
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. 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.
%K Energy Critical Waves
%K Cylindrical Domains
%K Dispersive Estimates
%K Strichartz Estimates
%U http://www.oalib.com/paper/6890314