On some large global solutions to 3-D density-dependent Navier–Stokes system with slow variable: Well-prepared data

  • Marius Paicu

    Université Bordeaux 1, Institut de Mathématiques de Bordeaux, F-33405 Talence Cedex, France
  • Ping Zhang

    Academy of Mathematics & Systems Science and Hua Loo-Keng Key Laboratory of Mathematics, The Chinese Academy of Sciences, Beijing 100190, China

Abstract

In this paper, we consider the global wellposedness of 3-D incompressible inhomogeneous Navier–Stokes equations with initial data slowly varying in the vertical variable, that is, initial data of the form for some and ε being sufficiently small. We remark that initial data of this type does not satisfy the smallness conditions in [11,18] no matter how small ε is.

Cite this article

Marius Paicu, Ping Zhang, On some large global solutions to 3-D density-dependent Navier–Stokes system with slow variable: Well-prepared data. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 4, pp. 813–832

DOI 10.1016/J.ANIHPC.2014.03.006