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Estimates up to the boundary of a weak solution to the Navier-Stokes equation in a cube in dependence on eigenvalues of the rate of deformation tensor. (English) Zbl 1101.35353

Mucha, Piotr (ed.) et al., Regularity and other aspects of the Navier-Stokes equations. Based on the conference on regularity and other qualitative aspects of the Navier-Stokes equations, Bȩdlewo, Poland, August 31–September 6, 2003. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 70, 185-197 (2005).
Summary: We formulate sufficient conditions for regularity up to the boundary of a weak solution \(v\) in a subdomain \(\Omega\times (t_1,t_2)\) of the time-space cylinder \(\Omega\times(0,T)\) by means of requirements on one of the eigenvalues of the rate of deformation tensor. We assume that \(\Omega\) is a cube.
For the entire collection see [Zbl 1081.35003].

MSC:

35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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