Global existence of smooth solution to evolutionary Faddeev model with short-pulse data

2025/11/04 by Luo, Shaoying, Wang, Jinhua, Wei, Changhua
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · doi:10.48550/arxiv.2511.17534

openalex publication_date 2025/11/04 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the Cauchy problem of the evolutionary Faddeev model, a system that maps from the Minkowski space ℝ¹⁺³ to the unit sphere \mathbbS². The model is a system of nonlinear wave equations whose nonlinearities exhibit a null structure and include semilinear terms, quasilinear terms, and the unknowns themselves. By considering a class of large initial data (in energy norm) of the short pulse type, we prove that the evolutionary Faddeev model admits a globally smooth solution via energy estimates. The main result is achieved through the selection of appropriate multipliers that are specially adapted to the geometry of the system.

Citations

• On global smooth solutions to the 2D isentropic and irrotational Chaplygin gases with short pulse data
• Large data global regularity for the 2+1-dimensional equivariant Faddeev model
• On the formation of shocks for quasilinear wave equations
• On classical global solutions of nonlinear wave equations with large data
• Sharp global regularity for the 2+1-dimensional equivariant Faddeev model
• A Large Data Regime for non-linear Wave Equations
• On the formation of trapped surfaces
• The Formation of Black Holes in General Relativity
• Some comments on the many-dimensional solitons

Related

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• Global existence for null-form wave equations with data in a Sobolev space of lower regularity and weight
• Global smooth solutions to 2D semilinear wave equations with large data