On Liouville type theorems in the stationary non-Newtonian fluids

초록

In this paper we prove a Liouville type theorem for the stationary equations of a non-Newtonian fluid in R3 with the viscous part of the stress tensor Ap(u)=div(|D(u)|p−2D(u)), where [Formula presented] and [Formula presented]. We consider a weak solution u∈Wloc1,p(R3) and its potential function V=(Vij)∈Wloc2,p(R3), i.e. ∇⋅V=u. We show that there exists a constant s0=s0(p) such that if the Ls mean oscillation of V for s>s0 satisfies a certain growth condition at infinity, then the velocity field vanishes. Our result includes the previous results [5,6] as particular cases. © 2021 Elsevier Inc.

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