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On the conditional regularity of the Navier-Stokes and related equations. (English) Zbl 1110.35312

Biler, Piotr (ed.) et al., Self-similar solutions of nonlinear PDE. Selected papers of the conference, Bȩdlewo, Poland, September 5–9, 2005. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 74, 117-126 (2006).
Summary: We present regularity conditions for a solution to the 3D Navier-Stokes equations, the 3D Euler equations and the 2D quasigeostrophic equations, considering the vorticity directions together with the vorticity magnitude. It is found that the regularity of the vorticity direction fields is most naturally measured in terms of norms of the Triebel-Lizorkin type.
For the entire collection see [Zbl 1104.35004].

MSC:

35Q35 PDEs in connection with fluid mechanics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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