In this paper we consider the equation for equivariant wave maps from R^{3+1} to S^3 and we prove global in forward time existence of certain C^infty - smooth solutions which have infinite critical Sobolev norm H^{3/2}(R^3)x H^{3/2}(R^3). Our construction provides solutions which can moreover satisfy the additional size condition |u(0,·)| L^infty(|x|geq1) > M for arbitrarily chosen M > 0. These solutions are also stable under suitable perturbations. Our method, strongly inspired by work of Krieger and Schlag, is based on a perturbative approach around suitably constructed approximate self-similar solutions.
A class of large global solutions for the wave-map equation
CHIODAROLI, ELISABETTA;
2017-01-01
Abstract
In this paper we consider the equation for equivariant wave maps from R^{3+1} to S^3 and we prove global in forward time existence of certain C^infty - smooth solutions which have infinite critical Sobolev norm H^{3/2}(R^3)x H^{3/2}(R^3). Our construction provides solutions which can moreover satisfy the additional size condition |u(0,·)| L^infty(|x|geq1) > M for arbitrarily chosen M > 0. These solutions are also stable under suitable perturbations. Our method, strongly inspired by work of Krieger and Schlag, is based on a perturbative approach around suitably constructed approximate self-similar solutions.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
1504.05051.pdf
accesso aperto
Descrizione: Versione post-print
Tipologia:
Documento in Post-print
Licenza:
Creative commons
Dimensione
218.56 kB
Formato
Adobe PDF
|
218.56 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.