On a strong solution of the non-stationary Navier-Stokes equations under slip or leak boundary conditions of friction type

By Takahito Kashiwabara. 2012

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Strong solutions of the non-stationary Navier-Stokes equations under non-linearized slip or leak boundary conditions are investigated. We show that the problems are formulated by a variational inequality of parabolic type, to which uniqueness is established. Using Galerkin's method and deriving a priori estimates, we prove global and local existence for 2D and 3D slip problems respectively. For leak problems, under no-leak assumption at $t=0$ we prove local existence in 2D and 3D cases. Compatibility conditions for initial states play a significant role in the estimates.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/9ae53666e1baac417c943e553dddf0bf0d6303a1