一类非线性抛物方程的衰减估计

Decay estimates of the nonlinear parabolic equation

研究由不可压缩非牛顿流体理论抽象出来的一类非线性抛物方程的Cauchy问题.主要利用Fourier分解方法讨论非线性抛物方程弱解的时间衰减性,证明了其解在L2范数下的衰减下界4为(1+t)-n ,从而与在相同初始条件下的线性热传导方程的解有同样的衰减下界.

This paper is concerned with the Cauchy problem of the nonliear parabolic equations which appears to be relevant in the theory of incompressible non-Newtonian fluids. Fourier splitting method is used to study the lower bounded of the weak solution and to prove that the weak solution decays in L^2 norm at (1+t)^(^(-n4)). So the decay rates coincide with the decay rates of the solutions to the heat equations with the same initial boundary data.