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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, Vladimir
Ivanov, 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
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 Mathematics
35 (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: 35L05
35B40
35P25
35J10
Appears in Collections:Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.35 (2003)

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