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The Steady Navier-Stokes System

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Equations of Motion for Incompressible Viscous Fluids

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

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Abstract

In this chapter, we are concerned with the steady Navier-Stokes systems with mixed boundary conditions involving Dirichlet, pressure, vorticity, stress and normal derivative of velocity together. As we have seen in Sect. 2.3.2, according to what kinds of bilinear forms for variational formulation are used, types of boundary conditions under consideration together are different. The variational formulations in Sect. 2.3.2 do not reflect, for example, the boundary conditions for stress and pressure together, but this case is important in practice.

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Authors and Affiliations

  1. Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People’s Republic of Korea

    Tujin Kim

  2. Guangzhou University and Institute of Applied Mathematics, Chinese Academy of Sciences, Guanzhou, Beijing, China

    Daomin Cao

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  1. Tujin Kim
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  2. Daomin Cao
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Correspondence to Tujin Kim .

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Kim, T., Cao, D. (2021). The Steady Navier-Stokes System. In: Equations of Motion for Incompressible Viscous Fluids. Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-78659-5_3

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