On regularity of a weak solution to the Navier–Stokes equations with the generalized Navier slip boundary conditions

0487356 - MÚ 2019 RIV US eng J - Journal Article
Neustupa, Jiří - Penel, P.
On regularity of a weak solution to the Navier–Stokes equations with the generalized Navier slip boundary conditions.
Advances in Mathematical Physics. Roč. 2018, March (2018), č. článku 4617020. ISSN 1687-9120. E-ISSN 1687-9139
R&D Projects: GA ČR(CZ) GA17-01747S
Institutional support: RVO:67985840
Keywords : Navier-Stokes equations
OECD category: Pure mathematics
Impact factor: 0.936, year: 2018
https://www.hindawi.com/journals/amp/2018/4617020/

The paper shows that the regularity up to the boundary of a weak solution 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 , (the positive part of ), and , where are the eigenvalues of the rate of deformation tensor . A regularity criterion in terms of the principal invariants of tensor is also formulated.
Permanent Link: http://hdl.handle.net/11104/0282022