SMALL DATA SOLUTIONS OF 2-D QUASILINEAR WAVE EQUATIONS UNDER NULL CONDITIONS

doi:10.1016/S0252-9602(17)30121-2

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (1): 125-150.doi: 10.1016/S0252-9602(17)30121-2

SMALL DATA SOLUTIONS OF 2-D QUASILINEAR WAVE EQUATIONS UNDER NULL CONDITIONS

刘颖博^1,2, Ingo WITT³

1. Department of Mathematics and IMS, Nanjing University, Nanjing 210093, China;
2. Department of Mathematics, China Pharmaceutical University, Nanjing 210009, China;
3. Mathematical Institute, University of Göttingen, Bunsenstr. 3-5, Göttingen 37073, Germany

收稿日期:2016-12-28 修回日期:2017-04-15 出版日期:2018-02-25 发布日期:2018-02-25
作者简介:Yingbo LIU,E-mail:lyb11206@163.com;Ingo WITT,E-mail:ingo.witt@mathematik.uni-goettingen.de
基金资助:
The research of LIU was partially supported by the NSFC (11571177) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. The research of WITT was partially funded by the DFG through the Sino-German Project "Analysis of PDEs and Applications".

SMALL DATA SOLUTIONS OF 2-D QUASILINEAR WAVE EQUATIONS UNDER NULL CONDITIONS

Yingbo LIU^1,2, Ingo WITT³

1. Department of Mathematics and IMS, Nanjing University, Nanjing 210093, China;
2. Department of Mathematics, China Pharmaceutical University, Nanjing 210009, China;
3. Mathematical Institute, University of Göttingen, Bunsenstr. 3-5, Göttingen 37073, Germany

Received:2016-12-28 Revised:2017-04-15 Online:2018-02-25 Published:2018-02-25
Supported by:
The research of LIU was partially supported by the NSFC (11571177) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. The research of WITT was partially funded by the DFG through the Sino-German Project "Analysis of PDEs and Applications".

摘要/Abstract

摘要：

For the 2-D quasilinear wave equation satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation (∂_t²-△_x)u+ satisfying null conditions with small initial data and the coefficients depending simultaneously on u and ∂u. Through construction of an approximate solution, combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction.

关键词: global existence, null condition, weighted energy estimate, continuous induction

Abstract:

Key words: global existence, null condition, weighted energy estimate, continuous induction

刘颖博, Ingo WITT. SMALL DATA SOLUTIONS OF 2-D QUASILINEAR WAVE EQUATIONS UNDER NULL CONDITIONS[J]. 数学物理学报(英文版), 2018, 38(1): 125-150.

Yingbo LIU, Ingo WITT. SMALL DATA SOLUTIONS OF 2-D QUASILINEAR WAVE EQUATIONS UNDER NULL CONDITIONS[J]. Acta mathematica scientia,Series B, 2018, 38(1): 125-150.

参考文献

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SMALL DATA SOLUTIONS OF 2-D QUASILINEAR WAVE EQUATIONS UNDER NULL CONDITIONS

SMALL DATA SOLUTIONS OF 2-D QUASILINEAR WAVE EQUATIONS UNDER NULL CONDITIONS

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