Scattering for Radial, Semi-Linear, Super-Critical Wave Equations with Bounded Critical Norm
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| 003 | CHVBK | ||
| 005 | 20210128100711.0 | ||
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| 008 | 210128e20151201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00205-015-0886-6 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0886-6 | ||
| 245 | 0 | 0 | |a Scattering for Radial, Semi-Linear, Super-Critical Wave Equations with Bounded Critical Norm |h [Elektronische Daten] |c [Benjamin Dodson, Andrew Lawrie] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 700 | 1 | |a Dodson |D Benjamin |u Department of Mathematics, Johns Hopkins University, 404 Krieger Hall, 3400 N. Charles Street, 21218, Baltimore, MD, USA |4 aut | |
| 700 | 1 | |a Lawrie |D Andrew |u Department of Mathematics, The University of California, Berkeley 970 Evans Hall #3840, 94720, Berkeley, CA, USA |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/3(2015-12-01), 1459-1529 |x 0003-9527 |q 218:3<1459 |1 2015 |2 218 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0886-6 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0886-6 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Dodson |D Benjamin |u Department of Mathematics, Johns Hopkins University, 404 Krieger Hall, 3400 N. Charles Street, 21218, Baltimore, MD, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Lawrie |D Andrew |u Department of Mathematics, The University of California, Berkeley 970 Evans Hall #3840, 94720, Berkeley, CA, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/3(2015-12-01), 1459-1529 |x 0003-9527 |q 218:3<1459 |1 2015 |2 218 |o 205 | ||