Global well-posedness for nonlinear wave equations with supercritical source and damping terms
Article
Guo, Y. (2019). Global well-posedness for nonlinear wave equations with supercritical source and damping terms
. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 477(2), 1087-1113. 10.1016/j.jmaa.2019.05.002
Guo, Y. (2019). Global well-posedness for nonlinear wave equations with supercritical source and damping terms
. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 477(2), 1087-1113. 10.1016/j.jmaa.2019.05.002
We prove the global well-posedness of weak solutions for nonlinear wave equations with supercritical source and damping terms on a three-dimensional torus T3 of the prototype utt−Δu+|ut|m−1ut=|u|p−1u,(x,t)∈T3×R+;u(0)=u0∈H1(T3)∩Lm+1(T3),ut(0)=u1∈L2(T3), where 1≤p≤min{ [Formula presented]m+ [Formula presented],m}. Notably, p is allowed to be larger than 6.