Low Regularity Well-Posedness for Nonlinear Wave Equations

Klainerman S,Machedon M.Space-time estimates for null forms and the local existence theorem [J].Comm Pure Appl Math,1993.1 221-1 268.[2] Ponce G,Sideris C D.Local regularity of nonlinear wave equations in three dimensions [J].Comm in Partial Differential Equations,1993,18:169-177.[3] Zhou Y.Local existence with minimal regularity for nonlinear wave equations[J].American J of Math,1997,119:671-703.[4] Lindblad H.A sharp counterexample to the local existence of low-regularity solutions to nonlinear wave equations[J].Duke Math J,1993,72:503-539.[5] Bournaveas N.Local existence of energy class solutions for the Dirac-Klein-Gordon equations [J].Comm in Partial Differential Equations,1999,24:1 167-1 193.[6] Bourgain J.Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations[J].Ⅰ,Ⅱ,Geom Funct Anal,1993,3:107-156,202-262.[7] Klainerman S,Machedon M.Smoothing estimates for null forms and applications[J].Duke Math J,1995,81:99-133.[8] Klainerman S,Selberg S.Remark on the optimal regularity for equations of wave maps type [J].Comm in Partial Differential Equations,1997,22:901-918.[9] Christ M,Colliander J,Tao T.Ⅲ posedness for nonlinear schrodinger and wave equations[J/OL].Http://www.Axxiv.math.AP/0311048.