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On the Wellposedness of Three-Dimensional Inhomogeneous Navier–Stokes Equations in the Critical Spaces

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Abstract

We prove the local wellposedness of three-dimensional incompressible inhomogeneous Navier–Stokes equations with initial data in the critical Besov spaces, without assumptions of small density variation. Furthermore, if the initial velocity field is small enough in the critical Besov space \({\dot B^{1/2}_{2,1}(\mathbb{R}^3)}\) , this system has a unique global solution.

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Authors and Affiliations

  1. Dértement de Mathématiques, Faculté des Sciences de Tunis Campus Universitaire, Tunis, 2092, Tunisia

    Hammadi Abidi

  2. Department of Mathematics, Jiangsu University, Zhenjiang, 212013, People’s Republic of China

    Guilong Gui

  3. The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Guilong Gui

  4. Academy of Mathematics & Systems Science and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Ping Zhang

Authors
  1. Hammadi Abidi
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  2. Guilong Gui
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  3. Ping Zhang
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Correspondence to Ping Zhang.

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Communicated by V. Šveràk

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Abidi, H., Gui, G. & Zhang, P. On the Wellposedness of Three-Dimensional Inhomogeneous Navier–Stokes Equations in the Critical Spaces. Arch Rational Mech Anal 204, 189–230 (2012). https://doi.org/10.1007/s00205-011-0473-4

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  • DOI: https://doi.org/10.1007/s00205-011-0473-4

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