A basic inequality for the Stokes operator related to the Navier boundary condition

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Abstract

We show that {norm of matrix} A u + Δ u {norm of matrix}L2 (Ωε) ≤ C (ε {norm of matrix} ∇ u {norm of matrix}L2 (Ωε) + {norm of matrix} u {norm of matrix}L2 (Ωε)), where Ωε is a thin domain in R3 of depth ε, the vector field u belongs to the domain of A, which is the Stokes operator for divergence-free vector fields on Ωε satisfying the Navier boundary condition.

Original languageEnglish
Pages (from-to)2585-2594
Number of pages10
JournalJournal of Differential Equations
Volume245
Issue number9
DOIs
StatePublished - Nov 1 2008

Keywords

  • Commutator estimate
  • Navier boundary condition
  • Stokes operator
  • Thin domain

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