Global Regularity to the Navier-Stokes Equations for A Class of Large Initial Data

2015/03/19 by Chen, Yukang, Han, Bin, Lei, Zhen
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.05659

Abstract

We prove that for initial data of the form u₀^ε(x) = (v₀^h(x_ε), ε^-1v₀ⁿ(x_ε))^T, x_ε= (x_h, εx_n)^T, n ≥ 4, the Cauchy problem of the incompressible Navier-Stokes equations on ℝⁿ is globally well-posed for all small ε> 0, provided that the initial velocity profile v₀ is analytic in x_n and certain norm of v₀ is sufficiently small but independent of ε.

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