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 mapsHs-spacesblow-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 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 $\alpha\in (0, 1 − \epsilon)$.
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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