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Mathematical results for some models of turbulence with critical and subcritical regularizations
In this paper, we establish the existence of a unique "regular" weak solution
to turbulent flows governed by a general family of models with
critical regularizations. In particular this family contains the simplified
Bardina model and the modified Leray- model. When the regularizations
are subcritical, we prove the existence of weak solutions and we establish an
upper bound on the Hausdorff dimension of the time singular set of those weak
solutions. The result is an interpolation between the bound proved by Scheffer
for the Navier-Stokes equations and the regularity result in the critical case