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- W2914374219 abstract "In this paper we prove a Liouville type theorem for generalized stationary Navier-Stokes systems in $Bbb R^3$, which model non-Newtonian fluids, where the Laplacian term $Delta u$ is replaced by the corresponding non linear operator $bA_p( u)=nabla cdot ( |bD(u)|^{p-2} bD(u))$ with $ bD(u) = frac{1}{2} (nabla u + (nabla u)^{ top})$, $3/2<p< 3$. In the case $3/2< ple 9/5$ we show that a suitable weak solution $uin W^{1, p}(Bbb R^3)$ satisfying $ liminf_{R rightarrow infty} |u_{ B(R)}| =0$ is trivial, i.e. $uequiv 0$. On the other hand, for $9/5<p<3$ we impose the condition for the Liouville type theorem in terms of a potential function: if there exists a matrix valued potential function $bV$ such that $ nabla cdot bV =u$, whose $L^{frac{3p}{2p-3}} $ mean oscillation has the following growth condition at infinity, $$ intmw_{B(r)} |bV- bV_{ B(r)} |^{frac{3p}{2p-3}} dx le C r^{frac{9-4p}{2p-3}}quad forall 1< r< +infty, $$ then $uequiv 0$. In the case of the Navier-Stokes equations, $p=2$, this improves the previous results in the literature." @default.
- W2914374219 created "2019-02-21" @default.
- W2914374219 creator A5041354678 @default.
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- W2914374219 date "2018-11-22" @default.
- W2914374219 modified "2023-09-27" @default.
- W2914374219 title "On Liouville type theorem for a generalized stationary Navier-Stokes equations" @default.
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