caa a22 4500 467989303 CHVBK 20180323112540.0 cr unu---uuuuu 170328e19900601xx s 000 0 eng 10.1007/BF01302932 doi (NATIONALLICENCE)springer-10.1007/BF01302932 Gao Jianmin Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Ontario, Canada aut A theorem of global existence of solutions to nonlinear wave equations in four space dimensions [Elektronische Daten] [Jianmin Gao] In this paper, the following nonlinear wave equation is considered; □u=F(u, D u, D x D u),x∈R n ,t>0; u=u 0 (x), u t =u 1 (x), t=0. We prove that if the space dimensionn ≥ 4 and the nonlinearityF is smooth and satisfies a mild condition in a small neighborhood of the origin, then the above problem admits a unique and smooth global solution (in time) whenever the initial data are small and smooth. The strategy in proof is to use and improve Global Sobolev Inequalities in Minkowski space (see [8]), and to develop a generalized energy estimate for solutions. Springer-Verlag, 1990 Monatshefte für Mathematik Springer-Verlag 109/2(1990-06-01), 123-134 0026-9255 109:2<123 1990 109 605 https://doi.org/10.1007/BF01302932 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01302932 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Gao Jianmin Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Ontario, Canada aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer-Verlag 109/2(1990-06-01), 123-134 0026-9255 109:2<123 1990 109 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer