ALMOST CONSERVATION LAWS AND GLOBAL ROUGH SOLUTIONS OF THE DEFOCUSING NONLINEAR WAVE EQUATION ON R^2  

作　　者：张再云 黄建华 孙明保 

机构地区：[1]School of Mathematics, Hunan Institute of Science and Technology [2]College of Science, National University of Defense Technology

出　　处：《Acta Mathematica Scientia》2017年第2期385-394,共10页数学物理学报（B辑英文版）

基　　金：supported by Hunan Provincial Natural Science Foundation of China(2016JJ2061);Scientific Research Fund of Hunan Provincial Education Department(15B102);China Postdoctoral Science Foundation(2013M532169,2014T70991);NNSF of China(11671101,11371367,11271118);the Construct Program of the Key Discipline in Hunan Province(201176);the aid program for Science and Technology Innovative Research Team in Higher Education Institutions of Hunan Province(2014207)

摘　　要：In this article, we investigate the initial value problem（IVP） associated with the defocusing nonlinear wave equation on R^2 as follows：{δttu-△u=-u^3 u（0,x）=u0（x）,δtu＊（0,x）=u1（x,）where the initial data （uo,ul）∈H^s-1（R^2）It is shown that the IVP is global well-posedness in H^s（R^2）×H^s-1×H^s-1（R^2）for any 1 〉 s 〉2/5.The proof relies upon the almost conserved quantity in using multilinear correction term. The main difficulty is to control the growth of the variation of the almost conserved quantity. Finally, we utilize linear-nonlinear decomposition benefited from the ideas of Roy [1].In this article, we investigate the initial value problem（IVP） associated with the defocusing nonlinear wave equation on R^2 as follows：{δttu-△u=-u^3 u（0,x）=u0（x）,δtu＊（0,x）=u1（x,）where the initial data （uo,ul）∈H^s-1（R^2）It is shown that the IVP is global well-posedness in H^s（R^2）×H^s-1×H^s-1（R^2）for any 1 〉 s 〉2/5.The proof relies upon the almost conserved quantity in using multilinear correction term. The main difficulty is to control the growth of the variation of the almost conserved quantity. Finally, we utilize linear-nonlinear decomposition benefited from the ideas of Roy [1].

关 键 词：Defocusing nonlinear wave equation global well-posedness I-METHOD linear-nonlinear decomposition below energy space 

分 类 号：O175[理学—数学]