Global well-posedness of 3-D inhomogeneous Navier–Stokes system with ill-prepared initial data

Ping Zhang; Zhifei Zhang

doi:10.4171/rmi/988

JournalsrmiVol. 34, No. 1pp. 355–395

Global well-posedness of 3-D inhomogeneous Navier–Stokes system with ill-prepared initial data

Ping Zhang
Chinese Academy of Sciences, Beijing, China
Zhifei Zhang
Peking University, Beijing, China

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Abstract

In this paper, we investigate the global well-posedness of 3-D incompressible inhomogeneous Navier–Stokes system with ill-prepared initial data of the form

(1 + ϵ^{β} a_{0} (x_{h}, ϵ x_{3}), (ϵ^{1 - α} v_{0}^{h}, ϵ^{- α} v_{0}^{3}) (x_{h}, ϵ x_{3}))

for any $α \in] 0, 1/3 [, β > 2 α$ , and $ϵ$ being sufficiently small. This result improves the global well-posedness result for so-called well-prepared initial data, which corresponds to the case of $α = 0$ .

Cite this article

Ping Zhang, Zhifei Zhang, Global well-posedness of 3-D inhomogeneous Navier–Stokes system with ill-prepared initial data. Rev. Mat. Iberoam. 34 (2018), no. 1, pp. 355–395

DOI 10.4171/RMI/988