论文标题
具有可变幂律指数的通用牛顿流体的强溶液的时间衰减
Temporal decay of strong solutions for generalized Newtonian fluids with variable power-law index
论文作者
论文摘要
我们考虑了在r^3中类似幂律的通用牛顿流体的运动，其中幂律指数是可变函数。这种非线性偏微分方程的系统是在电流动流体的数学模型中产生的。本文的目的是根据傅立叶分裂方法研究模型强溶液的衰减特性。我们首先证明溶液的L^2-Norm具有衰减率（1 + T）^{ - 3/4}。如果初始数据的h^1-norm足够小，我们进一步表明，溶液的衍生物在l^2-norm中以速率（1 + t）^{ - 5/4}衰减。
We consider the motion of a power-law-like generalized Newtonian fluid in R^3, where the power-law index is a variable function. This system of nonlinear partial differential equations arises in mathematical models of electrorheological fluids. The aim of this paper is to investigate the decay properties of strong solutions for the model, based on the Fourier splitting method. We first prove that the L^2-norm of the solution has the decay rate (1 + t)^{-3/4}. If the H^1-norm of the initial data is sufficiently small, we further show that the derivative of the solution decays in L^2-norm at the rate (1 + t)^{-5/4}.
