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Viscosity versus vorticity stretching: global well-posedness for a family of Navier-Stokes-alpha-like models. (English) Zbl 1110.76011
Summary: We study global well-posedness and regularity of solutions for a family of incompressible three-dimensional Navier-Stokes-alpha-like models that employ fractional Laplacian operators. This family of equations depends on two parameters, $$\theta _{1}$$ and $$\theta _{2}$$, which affect the strength of nonlinearity (vorticity stretching) and the degree of viscous smoothing. Varying $$\theta _{1}$$ and $$\theta _{2}$$ interpolates between the incompressible Navier-Stokes equations and the incompressible (Lagrangian averaged) Navier-Stokes-$$\alpha$$ model. Our main result, which contains previously established results of J.L. Lions and others, provides a relationship between $$\theta _{1}$$ and $$\theta _{2}$$ that is sufficient to guarantee global existence, uniqueness and regularity of solutions.

##### MSC:
 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 35Q30 Navier-Stokes equations
##### Keywords:
existence; uniqueness; regularity
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##### References:
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