On an anisotropic serrin criterion for weak solutions of the navier-stokes equations

Guillaume Lévy (1)

1 LJLL - Laboratoire Jacques-Louis Lions

In this paper, we draw on the ideas of [5] to extend the standard Serrin criterion [17] to an anisotropic version thereof. Because we work on weak solutions instead of strong ones, the functions involved have low regularity. Our method summarizes in a joint use of a uniqueness lemma in low regularity and the existence of stronger solutions. The uniqueness part uses duality in a way quite similar to the DiPerna-Lions theory, first developed in [7]. The existence part relies on L p energy estimates, whose proof may be found in [5], along with an approximation procedure.

Domaines: Equations aux dérivées partielles [math.AP]

Guillaume Lévy. On an anisotropic serrin criterion for weak solutions of the navier-stokes equations. 2017. ⟨hal-01462853⟩