The Glassey conjecture for nontrapping obstacles

2013/12/28 by Chengbo Wang, Wang, Chengbo
Mathematics · #35L15 #35L70 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1312.7433

openalex publication_date 2013/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We verify the three-dimensional Glassey conjecture for exterior domain (M, g), where the metric g is asymptotically Euclidean, provided that certain local energy assumption is satisfied. The radial Glassey conjecture exterior to a ball is also verified for dimension three or higher. The local energy assumption is satisfied for many important cases, including exterior domain with nontrapping obstacles and flat metric, exterior domain with star-shaped obstacles and small asymptotically Euclidean metric, as well as the nontrapping asymptotically Euclidean manifolds (Rⁿ, g).

Citations

• Grazing rays and reflection of singularities of solutions to wave equations

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