Dynamics of Partial Differential Equations
Volume 9 (2012)
On the Hausdorff dimension of singular sets for the Leray-α Navier-Stokes equations with fractional regularization
Pages: 261 – 271
We consider a family of Leray-α models with periodic boundary conditions in three space dimensions. Such models are a regularization, with respect to a parameter θ, of the Navier-Stokes equations. In particular, they share with the original equation (NS) the property of existence of global weak solutions. We establish an upper bound on the Hausdorff dimension of the time singular set of those weak solutions when θ is subcritical. The result is an interpolation between the bound proved by Scheffer for the Navier-Stokes equations and the regularity result proved in .
turbulence models, weak solution, singular set, Hausdorff measure
2010 Mathematics Subject Classification
35Q30, 35Q35, 76F60