Global and local theory of skew mean curvature flows

2020/10/27 by Ze Li, Li, Ze
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2010.14011

openalex publication_date 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the skew mean curvature flow. The results are threefold. First, we prove the global regularity of solutions with initial data which are small perturbations of planes in Sobolev spaces. Second, we prove the modified scattering and the existence of wave operators for small data, which completely determines the set of asymptotic states. Third, we study the Cauchy problem for arbitrary large data.

Related

• Global regularity of Skew mean curvature flow for small data in d≥ 4 dimensions
• Local well-posedness of the skew mean curvature flow for large data
• Local well-posedness of the Skew mean curvature flow for small data in d≥ 2 dimensions
• Global transversal stability of Euclidean planes under skew mean curvature flow evolutions
• Global well-posedness in the critical Besov space of the skew mean curvature flow in ℝ^d: d≥ 5