The Glassey conjecture for nontrapping obstacles

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Wang, Chengbo

关键词: Glassey conjecture;    Exterior domain;    Semilinear wave equations;    Local energy estimates;    KSS estimates;    Asymptotically Euclidean manifold;   

DOI  :  10.1016/j.jde.2015.02.023

来源: Elsevier

【 摘 要 】

We verify the 3-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 fiat metric, exterior domain with star-shaped obstacle and small asymptotically Euclidean metric, as well as the nontrapping asymptotically Euclidean manifolds (R-n, g) . (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free