R^2上一类非牛顿流体动力学方程组解的最优衰减率

Sharp Rate of Decay for Solutions to Non-Newtonian Fluid in R^2

本文利用Fourier分解方法讨论一类二维不可压缩非牛顿流体动力学方程组弱解的衰减性,证明了弱解在L^2范数下衰减率为(1+t)^(-1/2),和线性热传导方程解的衰减率一致,在此意义下本文的结果是最优的。

In this paper the authors study the decay rate for weak solutions to a class of the incompressible non-Newtonian fluids in R^2, and prove that the weak solutions decay in L^2 norm at （1＋t）^1/2. The estimate for the decay rate is sharp in the sense that it coincides with that of the solution to a linear heat equation.