Optimal lower bound estimates for the blow-up rate for the Zakharov system in a nonhomogeneous medium

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:380

Article

Gan, Zaihui^1,2  Guo, Boling²  Han, Lijia² 

[1] Sichuan Normal Univ, Coll Math & Software Sci, Chengdu 610068, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China

关键词: Zakharov system;    Nonhomogeneous medium;    Blow-up rate;    Optimal lower bound estimate;   

DOI  :  10.1016/j.jmaa.2011.02.052

来源: Elsevier

【 摘 要 】

In this paper we obtain lower bound estimates for the blow-up rate of finite time blow-up solutions to the Cauchy problem for the Zakharov system in a nonhomogeneous medium in two space dimensions. By introducing suitable scale transformations of space and time, and the use of compactness arguments, we derive an optimal lower bound estimate in the energy space H-2(R-2) x L-2(R-2) x H-1 (R-2) for the blow-up rate for t near the finite blow-up time T. Also we give an application to the virial identity for the Zakharov system under study. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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