Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4193

 Title: Concentration of Local Energy for Two-dimensional Wave Maps Authors: Georgiev, VladimirIvanov, Angel Keywords: equivariant wave mapsHs-spacesblow-up of solution Issue Date: 2003 Publisher: Università degli Studi di Trieste. Dipartimento di Matematica e Informatica Citation: Vladimir Georgiev and Angel Ivanov, "Concentration of Local Energy for Two-dimensional Wave Maps", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 35 (2003), pp. 195–235. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics35 (2003) Abstract: We construct some particular kind of solution to the two - dimensional equivariant wave map problem with inhomogeneous source term in space-time domain of type $\Omega_\alpha(t) = {x \in \mathbb R^2 : |x|^\alpha < t}$, where $\alpha\in (0, 1]$. More precisely, we take the initial data $(u_0, u_1)$ at time T in the space $H^{1+\epsilon} \times H^\epsilon$ with some $\epsilon > 0$. The source term is in $L^1((0, T); H^\epsilon(\Omega_\alpha(t)))$ and we show that the $H^{1+\epsilon}$ -norm of the solution blows-up, when $t \rightarrow 0_+$ and $\alpha\in (0, 1 − \epsilon)$. URI: http://hdl.handle.net/10077/4193 ISSN: 0049-4704 MS Classification: 35L0535B4035P2535J10 Appears in Collections: Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.35 (2003)

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