Concentration of local energy for two-dimensional wave maps

Vladimir Simeonov Gueorguiev; Angel Ivanov

Concentration of local energy for two-dimensional wave maps

Vladimir Simeonov Gueorguiev, Angel Ivanov

Research output: Contribution to journal › Article › peer-review

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 Ω_α(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 H^1+ε × H^ε with some ε > 0. The source term is in L¹((0, T);H^ε (Ω_α(t))) and we show that the H^1+ε - norm of the solution blows-up, when t → 0₊ and α ∈ (0, 1-ε).

Original language	English
Pages (from-to)	195-235
Number of pages	41
Journal	Rendiconti dell'Istituto di Matematica dell'Universita di Trieste
Volume	35
Publication status	Published - 2003 Jan 1
Externally published	Yes

Keywords

Blow-up of solution
Equivariant wave maps
H-spaces

ASJC Scopus subject areas

Mathematics(all)

Cite this

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title = "Concentration of local energy for two-dimensional wave maps",

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);Hε (Ωα(t))) and we show that the H1+ε - norm of the solution blows-up, when t → 0+ and α ∈ (0, 1-ε).",

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T1 - Concentration of local energy for two-dimensional wave maps

AU - Gueorguiev, Vladimir Simeonov

AU - Ivanov, Angel

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N2 - 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);Hε (Ωα(t))) and we show that the H1+ε - norm of the solution blows-up, when t → 0+ and α ∈ (0, 1-ε).

AB - 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);Hε (Ωα(t))) and we show that the H1+ε - norm of the solution blows-up, when t → 0+ and α ∈ (0, 1-ε).

KW - Blow-up of solution

KW - Equivariant wave maps

KW - H-spaces

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ER -

Concentration of local energy for two-dimensional wave maps

Abstract

Keywords

ASJC Scopus subject areas

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