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

Ping Zhang ^[1] ; Zhifei Zhang ^[2]
1. [1] Chinese Academy of Sciences
  
  Chinese Academy of Sciences
  
  China
2. [2] Peking University
  
  Peking University
  
  China
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 1, 2018, págs. 355-395
Idioma: inglés
DOI: 10.4171/RMI/988
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Resumen
- 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+ϵβa0(xh,ϵx3),(ϵ1−αvh0,ϵ−αv30)(xh,ϵx3)) for any α∈]0,1/3[,β>2α, 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.