Global well-posedness of weak solutions to the incompressible Euler equations with helical symmetry in ℝ³

2023/01/04 by Dengjun Guo, Lifeng Zhao, Guo, Dengjun +1
Earth and Planetary Sciences · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2301.01399

openalex publication_date 2023/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the three-dimensional incompressible Euler equation \\beginaligned amp;∂_t Ω+U ⋅ ∇ Ω+Ω⋅ ∇ U=0
amp;Ω(x,0)=Ω₀(x) \endaligned. in the whole space ℝ³. Under the assumption that the initial velocity is helical and without swirl, we prove the global well-posedness of weak solutions in L¹₁ \bigcap L^∞₁(ℝ³). The vortex transport formula is also obtained in our article.

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