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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
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