On wave systems with antisymmetric potential in dimension d >= 4 and well-posedness for (half-)wave maps

2024/04/30 by Silvino Reyes Farina, Armin Schikorra, Farina, Silvino Reyes +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.19421

openalex publication_date 2024/04/30 · openalex created_date 2024/05/03 · openalex updated_date 2026/07/28

Abstract

We prove a priori estimates for wave systems of the type ∂_tt u - Δu = Ω⋅ du + F(u) in ℝ^d × ℝ where d ≥ 4 and Ω is a suitable antisymmetric potential. We show that the assumptions on Ω are applicable to wave- and half-wave maps, the latter by means of the Krieger-Sire reduction. We thus obtain well-posedness of those equations for small initial data in H^(d)/(2)(ℝ^d).

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