非牛顿粘性不可压流方程的近似惯性流形(英文)

Approximate Inertial Manifolds of Non Newtonian Viscous Incompressible Fluids

本文利用对非牛顿粘性不可压缩流方程对时间 t的解析性和长时间渐近性估计 ,具体构造了它的近似惯性流形 ,并得出收敛阶估计 .

The concept of approximate inertial manifolds is related to the study of the long time behaviour of partial differential equations. In this paper, we obtain the analyticity in time and the behavior of higher modes of the solution and then construct some approximate inertial manifolds for the nonlinear system of equations describing the motion of a bipolar incompressible viscous fluids. Here, we consider only the case of a spatially periodic velocity field, the viscous part of the stress tensor is generally a nonlinear function of the symmetric part of the velocity gradient, which describing this dependence satisfies the polynomial (p-1) growth condition. For 1<p≤2 the existence of an inertial manifold for the model was a known result. However, in the case of p>2, the existence of inertial manifold is still an open problem. The approximate inertial manifolds are invented to describe large time dynamics of the model for 2<p<114.