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 maps; Hs-spaces; blow-up of solution Issue Date: 2003 Publisher: Università degli Studi di Trieste. Dipartimento di Matematica e Informatica Source: 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 thetwo - dimensional equivariant wave map problem withinhomogeneous 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 sourceterm is in $L^1((0, T); H^\epsilon(\Omega_\alpha(t)))$ andwe show that the $H^{1+\epsilon}$ -norm of the solution blows-up,when $t \rightarrow 0_+$ and $\alpha\in (0, 1 − \epsilon)$. Type: Article URI: http://hdl.handle.net/10077/4193 ISSN: 0049-4704 Appears in Collections: Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.35 (2003)

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