Almost global existence for semilinear wave equations with mixed nonlinearities in four space dimensions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:459

Article

Wang, Chengbo¹  Zhou, Hao² 

[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

[2] Zhejiang Shuren Univ, Dept Basic Sci, Hangzhou 310015, Zhejiang, Peoples R China

关键词: Strauss conjecture;    Glassey conjecture;    Local energy estimates;    KSS estimates;   

DOI  :  10.1016/j.jmaa.2017.10.058

来源: Elsevier

【 摘 要 】

We study the long time existence for the small-amplitude semilinear wave equations with mixed nonlinearities of the form cilutr c(1)vertical bar u(t)vertical bar(p) with c(2)u(2) with p >= 2 when the spatial dimension is four. By exploiting the local energy estimates and their recent variants, we prove the almost global existence up to exp(c epsilon(-2)), which is sharp in general. For the case p is an element of (2, 3), due to technical reason, we need to assume the initial data to be radial. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free