The top-order energy of quasilinear wave equations in two space dimensions is uniformly bounded  

作　　者：Shijie Dong Philippe G.LeFloch Zhen Lei 

机构地区：[1]Southern University of Science and Technology,SUSTech International Center for Mathematics,and Department of Mathematics,Shenzhen 518055,China [2]Fudan University,School of Mathematical Sciences,220 Handan Road,Shanghai 200433,China [3]Laboratoire Jacques-Louis Lions and Centre National de la Recherche Scientifique,Sorbonne Université,4 Place Jussieu,Paris 75252,France [4]Shanghai Center for Mathematical Sciences,Shanghai 200433,China

出　　处：《Fundamental Research》2024年第2期270-283,共14页自然科学基础研究（英文版）

基　　金：supported by the China Postdoctoral Science Foundation(2021M690702);The author Z.L.was in part supported by NSFC(11725102);Sino-German Center(M-0548);the National Key R&D Program of China(2018AAA0100303)National Support Program for Young Top-Notch Talents;Shanghai Science and Technology Program[21JC1400600 and No.19JC1420101].

摘　　要：Alinhac solved a long-standing open problem in 2001 and established that quasilinear wave equations in two space dimensions with quadratic null nonlinearities admit global-in-time solutions,provided that the initial data are compactly supported and sufficiently small in Sobolev norm.In this work,Alinhac obtained an upper bound with polynomial growth in time for the top-order energy of the solutions.A natural question then arises whether the time-growth is a true phenomenon,despite the possible conservation of basic energy.In the present paper,we establish that the top-order energy of the solutions in Alinhac theorem remains globally bounded in time.

关 键 词：Quasilinear wave equation Global-in-time solution Uniform energy bounds Quadratic null nonlinearity Hyperboloidal foliation method Vector field method 

分 类 号：O17[理学—数学]