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The Full Nonlinear Navier-Stokes Equations

  • Hermann Sohr
Chapter
  • 1.8k Downloads
Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)

Abstract

In this chapter, \(\Omega \subseteq {\mathbb{R}^n}\) means a domain with n = 2 or n = 3, and [0, T) is a fixed time interval with 0 < T ≤ ∞. The full nonlinear Navier-Stokes system in [0, T) × Ω has the form
$$\begin{array}{*{20}{c}} {{u_t} - v\Delta u + u \cdot \nabla u + \nabla p}& = &f&,&{div u = 0,} \\ {u|\partial \Omega }& = &0&,&{u(0) = {u_0}} \end{array}$$
(1.1.1)
where the boundary condition u|∂Ω = 0 is omitted if Ω = ℝn. We refer to [Lad69, Chap. 6], [Tem77, Chap. III3], [Ama00] concerning weak solutions of these equations.

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Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Hermann Sohr
    • 1
  1. 1.Fachbereich Mathematik/InformatikUniversität PaderbornPaderbornSwitzerland

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