caa a22 4500 605515832 CHVBK 20210128100711.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00205-015-0886-6 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0886-6 Scattering for Radial, Semi-Linear, Super-Critical Wave Equations with Bounded Critical Norm [Elektronische Daten] [Benjamin Dodson, Andrew Lawrie] In this paper we study the focusing cubic wave equation in 1+5 dimensions with radial initial data as well as the one-equivariant wave maps equation in 1+3 dimensions with the model target manifolds $${\mathbb{S}^3}$$ S 3 and $${\mathbb{H}^3}$$ H 3 . In both cases the scaling for the equation leaves the $${\dot{H}^{\frac{3}{2}} \times \dot{H}^{\frac{1}{2}}}$$ H ˙ 3 2 × H ˙ 1 2 -norm of the solution invariant, which means that the equation is super-critical with respect to the conserved energy. Here we prove a conditional scattering result: if the critical norm of the solution stays bounded on its maximal time of existence, then the solution is global in time and scatters to free waves as $${t \to \pm \infty}$$ t → ± ∞ . The methods in this paper also apply to all supercritical power-type nonlinearities for both the focusing and defocusing radial semi-linear equation in 1+5 dimensions, yielding analogous results. Springer-Verlag Berlin Heidelberg, 2015 Dodson Benjamin Department of Mathematics, Johns Hopkins University, 404 Krieger Hall, 3400 N. Charles Street, 21218, Baltimore, MD, USA aut Lawrie Andrew Department of Mathematics, The University of California, Berkeley 970 Evans Hall #3840, 94720, Berkeley, CA, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/3(2015-12-01), 1459-1529 0003-9527 218:3<1459 2015 218 205 https://doi.org/10.1007/s00205-015-0886-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0886-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dodson Benjamin Department of Mathematics, Johns Hopkins University, 404 Krieger Hall, 3400 N. Charles Street, 21218, Baltimore, MD, USA aut NATIONALLICENCE 700 1- Lawrie Andrew Department of Mathematics, The University of California, Berkeley 970 Evans Hall #3840, 94720, Berkeley, CA, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/3(2015-12-01), 1459-1529 0003-9527 218:3<1459 2015 218 205