Infinite time blow-up for half-harmonic map flow from ℝ into \mathbbS¹

2017/11/15 by Yannick Sire, Juncheng Wei, Sire, Yannick +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1711.05387

openalex publication_date 2017/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study infinite time blow-up phenomenon for the half-harmonic map flow \u_t = -(-Δ)^(1)/(2)u + ((1)/(2π)∫_ℝ(|u(x)-u(s)|²)/(|x-s|²)ds)u in ℝ× (0, ∞), u(⋅, 0) = u₀ in ℝ, . with a function u:ℝ× [0, ∞)→ \mathbbS¹. Let q₁,⋯, q_k be distinct points in ℝ, there exist an initial datum u₀ and smooth functions ξ_j(t)→ q_j, 0

Citations

• Singularity formation for the two-dimensional harmonic map flow into S²

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