4.6 Article

Stability and instability of the 3D incompressible viscous flow in a bounded domain

Publisher

SPRINGER HEIDELBERG
DOI: 10.1007/s00526-022-02205-8

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Funding

  1. National Natural Science Foundation of China [12101305]
  2. priority academic program development of Jiangsu higher education institutions
  3. National Science Foundation [DMS-1813603, DMS-2108453]

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This paper investigates the stability and instability of the steady state for the 3D homogeneous incompressible viscous flow in a bounded simply connected domain with a smooth boundary. It is shown that there exists a critical slip length, below which the steady state is unstable, and above which it is stable.
In this paper, we investigate the stability and instability of the steady state (0, p(s)) (p(s) is a constant) for the 3D homogeneous incompressible viscous flow in a bounded simply connected domain with a smooth boundary where the velocity satisfies the Navier boundary conditions. It is shown that there exists a critical slip length -C-r mu, where C-r > 0 is an explicit generic constant depending only on the domain (given in (1.7)) and mu > 0 is the viscosity coefficient, such that when the slip length zeta is less than -C-r mu, the steady state (0, p(s)) is linearly and nonlinearly unstable; and conversely, the steady state (0, p(s)) is linearly and nonlinearly stable when zeta > -C-r mu.

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