Global existence and lifespan for semilinear wave equations with mixed nonlinear terms

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Dai, Wei¹  Fang, Daoyuan¹  Wang, Chengbo¹ 

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

关键词: Strauss conjecture;    Glassey conjecture;    Generalized Strichartz estimate;    Klainerman-Sobolev inequalities;   

DOI  :  10.1016/j.jde.2019.04.007

来源: Elsevier

【 摘 要 】

Firstly, we study the equation square u = vertical bar u vertical bar(qc) + vertical bar partial derivative u vertical bar(p) with small data, where q(c) is the critical power of Strauss conjecture and p >= q(c). We obtain the optimal estimate of the lifespan ln(T-epsilon) approximate to epsilon(-)(qc)(()(qc)(-1)) in n = 3, and improve the lower bound of T-epsilon from exp(c epsilon(-(qc-1))) to exp(c epsilon(-(qc-1)2/2)) in n = 2. Then, we study the Cauchy problem with small initial data for a system of semilinear wave equations square u = vertical bar v vertical bar(q), square v = vertical bar partial derivative(t)u vertical bar(p) in 3-dimensional space with q < 2. We obtain that this system admits a global solution above a p - q curve for spherically symmetric data. On the contrary, we get a new region where the solution will blow up. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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