A Comparison of Teaching Models in the West and in China

Models of teaching commonly used in the West and in China are analyzed and compared, using an analytical approach that systematically considers different aspects of the models. The purpose of the exploration is three-fold: (a) to create better understanding of both Chinese and Western models, for mutual insight and to strengthen the development of pedagogical theory building in China; (b) to guide a joint project between the Netherlands and China relative to the development computer-related learning resources for China; and (c) to contribute to better overall understanding of how instructional resources can be adapted for use in both Western and Chinese situations. The analysis provides a contribution for each of these goals

Global unique solvability of inhomogeneous Navier-Stokes equations with bounded density

In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for $d=2,3$) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from above and below by some positive constants, and with initial velocity $u_0\in H^s(\R^2)$ for $s>0$ in 2-D, or $u_0\in H^1(\R^3)$ satisfying |u_0|_{L^2}|\na u_0|_{L^2} being sufficiently small in 3-D. This in particular improves the most recent well-posedness result in [10], which requires the initial velocity $u_0\in H^2(\R^d)$ for the local well-posedness result, and a smallness condition on the fluctuation of the initial density for the global well-posedness result