This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in ?3. Based on linear L p -L q estimates, the auxiliary decay properties of the solutions and generalized Gronwall typ...This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in ?3. Based on linear L p -L q estimates, the auxiliary decay properties of the solutions and generalized Gronwall type arguments, some optimal upper and lower bounds for the decay of higher order derivatives of solutions are derived without assuming any decay properties of solutions and using Fourier splitting technology.展开更多
A concept map is a schematic device for representing a set of concept meanings embedded in a framework of propositions.It can be used to evaluate students’knowledge structure.This article introduces the comparative s...A concept map is a schematic device for representing a set of concept meanings embedded in a framework of propositions.It can be used to evaluate students’knowledge structure.This article introduces the comparative study of Chinese and American secondary school students’knowledge structure.They are compared quantitatively and qualitatively in terms of mean score,individual proposition scores,proposition choice and map structure.The results indicate that students’knowledge structures in the two countries are remarkably different.Compared with American students,Chinese students’ability to take an exam is stronger and their mean score is higher.However,Chinese students need to improve their general knowledge and creativity although their basic knowledge is solid and they are better in mastering discipline knowledge and knowledge application.展开更多
This paper is concerned with time decay problem of Ladyzhenskaya model governed incompressible viscous fluid motion with the dissipative potential having p-growth （p ≥ 3） in R^3. With the aid of the spectral decomp...This paper is concerned with time decay problem of Ladyzhenskaya model governed incompressible viscous fluid motion with the dissipative potential having p-growth （p ≥ 3） in R^3. With the aid of the spectral decomposition of the Stokes operator and L^p - L^q estimates, it is rigorously proved that the Leray-Hopf type weak solutions decay in L^2（R^3） norm like t-n/2（1/r-1/2） under the initial data uo ∈ L^2（R^3） ∩ L^r（R^3） for 1≤ r 〈 2. Moreover, the explicit error estimates of the difference between Ladyzhenskaya model and Navier-Stokes flow are also investigated.展开更多
基金the National Natural Science Foundation of China (Grant Nos.10241005,10771001)Natural Science Foundation of Department of Education in Anhui Province (Grant No.KJ2008A025)
文摘This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in ?3. Based on linear L p -L q estimates, the auxiliary decay properties of the solutions and generalized Gronwall type arguments, some optimal upper and lower bounds for the decay of higher order derivatives of solutions are derived without assuming any decay properties of solutions and using Fourier splitting technology.
文摘A concept map is a schematic device for representing a set of concept meanings embedded in a framework of propositions.It can be used to evaluate students’knowledge structure.This article introduces the comparative study of Chinese and American secondary school students’knowledge structure.They are compared quantitatively and qualitatively in terms of mean score,individual proposition scores,proposition choice and map structure.The results indicate that students’knowledge structures in the two countries are remarkably different.Compared with American students,Chinese students’ability to take an exam is stronger and their mean score is higher.However,Chinese students need to improve their general knowledge and creativity although their basic knowledge is solid and they are better in mastering discipline knowledge and knowledge application.
文摘This paper is concerned with time decay problem of Ladyzhenskaya model governed incompressible viscous fluid motion with the dissipative potential having p-growth （p ≥ 3） in R^3. With the aid of the spectral decomposition of the Stokes operator and L^p - L^q estimates, it is rigorously proved that the Leray-Hopf type weak solutions decay in L^2（R^3） norm like t-n/2（1/r-1/2） under the initial data uo ∈ L^2（R^3） ∩ L^r（R^3） for 1≤ r 〈 2. Moreover, the explicit error estimates of the difference between Ladyzhenskaya model and Navier-Stokes flow are also investigated.
