A class of large global solutions for the wave-map equation
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- by Elisabetta Chiodaroli and Joachim Krieger PDF
- Trans. Amer. Math. Soc. 369 (2017), 2747-2773 Request permission
Abstract:
In this paper we consider the equation for equivariant wave maps from $\mathbb {R}^{3+1}$ to $\mathbb {S}^3$ and we prove global in forward time existence of certain $C^\infty$-smooth solutions which have infinite critical Sobolev norm $\dot {H}^{\frac {3}{2}}(\mathbb {R}^3)\times \dot {H}^{\frac {1}{2}}(\mathbb {R}^3)$. Our construction provides solutions which can moreover satisfy the additional size condition $\|u(0, \cdot )\|_{L^\infty (|x|\geq 1)}>M$ 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.References
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Additional Information
- Elisabetta Chiodaroli
- Affiliation: EPFL Lausanne, Station 8, CH-1015 Lausanne, Switzerland
- MR Author ID: 935797
- Joachim Krieger
- Affiliation: EPFL Lausanne, Station 8, CH-1015 Lausanne, Switzerland
- MR Author ID: 688045
- Received by editor(s): April 22, 2015
- Published electronically: June 20, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 2747-2773
- MSC (2010): Primary 35L05
- DOI: https://doi.org/10.1090/tran/6805
- MathSciNet review: 3592527