任意流量剪切增稠流体的定常流动
Steady Flow for Shear Thickening Fluids with Arbitrary Fluxes
摘要：
本文求解了具有无界出口区域的粘性与剪切有关的非牛顿不可压缩流体的定常Navier-斯托克斯方程，其中粘性是剪切增稠的，即粘性由剪切速率的p-2次方给出，其中p>2。通量假定任意给定值，速度场的狄利克雷积分在区域的出口处至多线性增长。在“能量色散”的某些小条件下，我们还证明了该问题的解是唯一的。我们的结果是O.A. Ladyzhenskaya和VA。Solonnikov（J. Soviet Math.，21（1983）728-761）（p=2）。
英文摘要：
We solve the stationary Navier-Stokes equations for non-Newtonian incompressible fluids with shear dependent viscosty in domains with unbounded outlets, in the case of shear thickening viscosity, i.e. the viscosity is given by the shear rate to the power p-2 where p>2. The flux assumes arbitrary given values and the Dirichlet integral of the velocity field grows at most linearly in the outlets of the domain. Under some smallness conditions on the "energy dispersion" we also show that the solution of this problem is unique. Our results are an extension of those obtained by O.A. Ladyzhenskaya and V.A. Solonnikov (J. Soviet Math., 21 (1983) 728-761) for Newtonian fluids (p=2).
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