Viscosity versus vorticity stretching: Global well-posedness for a family of Navier–Stokes-alpha-like models
✍ Scribed by Eric Olson; Edriss S. Titi
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 420 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0362-546X
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✦ Synopsis
We study global well-posedness and regularity of solutions for a family of incompressible threedimensional Navier-Stokes-alpha-like models that employ fractional Laplacian operators. This family of equations depends on two parameters, θ 1 and θ 2 , which affect the strength of non-linearity (vorticity stretching) and the degree of viscous smoothing. Varying θ 1 and θ 2 interpolates between the incompressible Navier-Stokes equations and the incompressible (Lagrangian averaged) Navier-Stokes-α model. Our main result, which contains previously established results of J.L. Lions and others, provides a relationship between θ 1 and θ 2 that is sufficient to guarantee global existence, uniqueness and regularity of solutions.