Concentration of local energy for two-dimensional wave maps

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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 Ωα(t) = (x ∈ ℝ2: |x| α < t), where α ∈ (0, 1]. More precisely, we take the initial data (u0, u1) at time T in the space H1+ε × Hε with some ε > 0. The source term is in L1((0, T);Hεα(t))) and we show that the H1+ε - norm of the solution blows-up, when t → 0+ and α ∈ (0, 1-ε).

Original languageEnglish
Pages (from-to)195-235
Number of pages41
JournalRendiconti dell'Istituto di Matematica dell'Universita di Trieste
Volume35
Publication statusPublished - 2003 Jan 1
Externally publishedYes

Keywords

  • Blow-up of solution
  • Equivariant wave maps
  • H-spaces

ASJC Scopus subject areas

  • Mathematics(all)

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