Todorova, GrozdenaUğurlu, DavutYordanov, Borislav2021-06-232021-06-2320090025-5645https://doi.org/10.2969/jmsj/06120625https://hdl.handle.net/20.500.12491/4147We show that the nonlinear wave equation u + u 3 t = 0 is globally well-posed in radially symmetric Sobolev spaces H k rad(R 3) × H k-1 rad for all integers k > 2. This partially extends the well-posedness in H k(R 3) × H k-1(.R 3) for all k ? [1,2], established by Lions and Strauss [12]. As a consequence we obtain the global existence of C? solutions with radial C? 0 data. The regularity problem requires smoothing and non-concentration estimates in addition to standard energy estimates, since the cubic damping is critical when k = 2. We also establish scattering results for initial data (u,u t)| t=0 in radially symmetric Sobolev spaces. © 2009 The Mathematical Society of Japan.eninfo:eu-repo/semantics/openAccessNonlinear DampingRegularityWave EquationArticle10.2969/jmsj/061206256126256492-s2.0-67650932808Q1