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Navier-Stokes equations and area of interfaces. (English) Zbl 0725.35080

The author studies properties of solutions of the Navier-Stokes equations in three space dimensions.
New estimates for the vorticity (curl of the velocity) are derived. Using these estimates the author constructs global weak solutions to the Navier-Stokes equations. These solutions admit rather general vortex structures with arbitrarily large vorticity as initial conditions.
Using geometric measure theory and these new estimates, the author studies the two dimensional Hausdorff measure of level sets of vorticity magnitude. Also considered are areas of level sets of convected scalars, e.g., isotherms in Rayleigh-Benard convection.
Reviewer: A.J.Meir (Auburn)

MSC:

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI

References:

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