The Glassey conjecture for nontrapping obstacles

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 (R^n, g).

Final version, to appear in Journal of Differential Equations. 18 pages. Typos fixed, presentation polished and references added/updated

References in corpus (4)

• The Strauss conjecture on Kerr black hole backgrounds
• Global existence of null-form wave equations on small asymptotically Euclidean manifolds
• The Glassey conjecture on asymptotically flat manifolds
• Almost global existence for some semilinear wave equations with almost critical regularity