2021/02/28 by Lorenzo Brandolese
Engineering · Mathematics · #Astrophysics #Character (mathematics) #Classical mechanics #Compressibility #Computer science #Field (mathematics) #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Geometry #Hexagonal crystal system #Isotropy #Mathematics #Mechanics #Navier-Stokes equation solutions #Physics #Planar #Pure mathematics #Rest (music) #Saturn #Stability (learning theory) #math.AP
paper · pdf · doi:10.1080/03605302.2022.2037633
published in Communications in Partial Differential Equations 47(6), 1070-1097 (Taylor & Francis)
openalex publication_date 2022/03/02 · arxiv created 2022/03/07 · arxiv updated 2022/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Geometric structures naturally appear in fluid motions. One of the best known examples is Saturn's Hexagon, the huge cloud pattern at the level of Saturn's north pole, remarkable both for the regularity of its shape and its stability during the past decades. In this paper we will address the spontaneous formation of hexagonal structures in planar viscous flows, in the classical setting of Leray's solutions of the Navier-Stokes equations. Our analysis also makes evidence of the isotropic character of the energy density of the fluid for sufficently localized 2D flows in the far field: it implies, in particular, that fluid particles of such flows are nowhere at rest at large distances.