Global well-posedness for radial extremal hypersurface equation in (1+3 )-dimensional Minkowski space-time in critical Sobolev space

2022/12/17 by Sheng Wang, Yi Zhou, Wang, Sheng +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2212.08828

openalex publication_date 2022/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we prove the global well-posedness in the critical Sobolev space H_rad²(ℝ²) × H_rad¹ (ℝ²) for the radial time-like extremal hypersurface equation in (1+3)- dimensional Minkowski space-time. This is achieved by deriving a new div-curl type lemma and combined it with energy and ``momentum" balance law to get some space-time estimates of the nonlinearity.

Cited by

• Physical Space Proof of Bilinear Estimates and Applications to Nonlinear Dispersive Equations (II)

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