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Global Wellposedness for the 3D Inhomogeneous Incompressible Navier–Stokes Equations

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Abstract

This paper addresses the three-dimensional Navier–Stokes equations for an incompressible fluid whose density is permitted to be inhomogeneous. We establish a theorem of global existence and uniqueness of strong solutions for initial data with small \({\dot{H}^{\frac12}}\) -norm, which also satisfies a natural compatibility condition. A key point of the theorem is that the initial density need not be strictly positive.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4K1, Canada

    Walter Craig

  2. NCMIS, AMSS, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Xiangdi Huang

  3. Department of Pure and Applied Mathematics Graduate School of Information Science and Technology, Osaka University, Osaka, Japan

    Xiangdi Huang

  4. Department of Mathematics, Soochow University, 1 Shizi Street, Suzhou, 215006, Jiangsu, People’s Republic of China

    Yun Wang

Authors
  1. Walter Craig
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  2. Xiangdi Huang
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  3. Yun Wang
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Correspondence to Walter Craig.

Additional information

Communicated by S. Friedlander

The research of W. Craig is supported in part by a Killam Research Fellowship, the Canada Research Chairs Program and NSERC through grant number 238452–11. The research of X. D. Huang is partially supported by the National Center for Mathematics and Interdisciplinary Sciences, CAS and NNSFC Grant No.11101392. The research of Y. Wang is supported in part by a Canada Research Chairs Postdoctoral Fellowship at McMaster University and NNSFC Grant No. 11241004.

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Craig, W., Huang, X. & Wang, Y. Global Wellposedness for the 3D Inhomogeneous Incompressible Navier–Stokes Equations. J. Math. Fluid Mech. 15, 747–758 (2013). https://doi.org/10.1007/s00021-013-0133-6

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