On Regularity of a Weak Solution to the Navier–Stokes Equations with the Generalized Navier Slip Boundary Conditions

Jiří Neustupa and Patrick Penel

Advances in Mathematical Physics, 2018, vol. 2018, issue 1

Abstract: The paper shows that the regularity up to the boundary of a weak solution v of the Navier–Stokes equation with generalized Navier’s slip boundary conditions follows from certain rate of integrability of at least one of the functions ζ1, (ζ2) + (the positive part of ζ2), and ζ3, where ζ1 ≤ ζ2 ≤ ζ3 are the eigenvalues of the rate of deformation tensor D(v). A regularity criterion in terms of the principal invariants of tensor D(v) is also formulated.

Date: 2018
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https://doi.org/10.1155/2018/4617020

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:4617020

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