The role of spectral anisotropy in the resolution of the three-dimensional Navier-Stokes equations

2012/05/31 by Jean-Yves Chemin, Isabelle Gallagher, Chemin, Jean-Yves +3
Engineering · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1205.6992

openalex publication_date 2012/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present different classes of initial data to the three-dimensional, incompressible Navier-Stokes equations, which generate a global in time, unique solution though they may be arbitrarily large in the end-point function space in which a fixed-point argument may be used to solve the equation locally in time. The main feature of these initial data is an anisotropic distribution of their frequencies. One of those classes is taken from previous papers by two of the authors and collaborators, and another one is new.

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