On the Bardina's model in the whole space

Luigi Carlo Berselli (1) , Roger Lewandowski (2, 3)

1 DMA - Dipartimento di Matematica Applicata [Pisa]
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences

We consider the Bardina's model for turbulent incompressible flows in the whole space with a cutoff frequency of order α −1 > 0. We show that for any α > 0 fixed, the model has a unique regular solution defined for all t ∈ [0, ∞[.

Mots clés: Bardina's model; Helmholz filter; Navier-Stokes equations; regular solutions

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Luigi Carlo Berselli, Roger Lewandowski. On the Bardina's model in the whole space. Journal of Mathematical Fluid Mechanics, 2018, 20 (3), pp.1335-1351. ⟨10.1007/s00021-018-0369-2⟩. ⟨hal-01590760⟩