On the regularity of the solutions to the 3D Navier-Stokes equations: a remark on the role of the helicity. (English. Abridged French version) Zbl 1172.35051
Summary: We show that if velocity and vorticity are orthogonal at each point (and they become orthogonal fast enough) then solutions of the 3D Navier-Stokes equations are smooth. This condition implies that the helicity is identically zero and, in a certain sense, the flow resembles the 2D geometric situation.
MSC:
| 35Q30 | Navier-Stokes equations |
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
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