2024/06/23 by Daomin Cao, Cao, Daomin, Boquan Fan +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2406.16134
openalex publication_date 2024/06/23 · openalex created_date 2024/06/26 · openalex updated_date 2026/07/28
In this paper we present some classification results for the steady Euler equations in two-dimensional exterior domains with free boundaries. We prove that, in an exterior domain, if a steady Euler flow devoid of interior stagnation points adheres to slip boundary conditions and maintains a constant norm on the boundary, along with certain additional conditions at infinity, then the domain is the complement of a disk, and the flow is circular, namely the streamlines are concentric circles. Additionally, we establish that in the entire plane, if all the stagnation points of a steady Euler flow coincidentally form a disk, then, under certain additional reasonable conditions near the stagnation points and at infinity, the flow must be circular. The proof is based on a refinement of the method of moving planes.