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On the Regularity and Decay of the Weak Solutions to the Steady-State Navier-Stokes Equations in Exterior Domains

In: Applied Nonlinear Analysis

Author

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  • Frédéric Alliot
  • Cherif Amrouche

Abstract

In this article, we study the regularity properties of the weak solutions to the steady-state Navier-Stokes equations in exterior domains of ℝ3. Our approach is based on a combination of the properties of Stokes problems in ℝ3 and in bounded domains. We obtain in particular a decomposition result for the pressure and some sufficient conditions for the velocity to vanish at infinity.

Suggested Citation

  • Frédéric Alliot & Cherif Amrouche, 2002. "On the Regularity and Decay of the Weak Solutions to the Steady-State Navier-Stokes Equations in Exterior Domains," Springer Books, in: Adélia Sequeira & Hugo Beirão da Veiga & Juha Hans Videman (ed.), Applied Nonlinear Analysis, pages 1-18, Springer.
    • Handle: RePEc:spr:sprchp:978-0-306-47096-7_1
    DOI: 10.1007/0-306-47096-9_1
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