论文标题
轴对称域中Stokes方程近似的框架
A framework for approximation of the Stokes equations in an axisymmetric domain
论文作者
论文摘要
我们开发了一个框架来解决轴对称域中的固定，不可压缩的Stokes方程。通过相对于角变量的傅立叶扩展，三维的Stokes问题将减少为等效的，可计数的二维问题。通过使用三维Sobolev规范的分解，我们为二维问题得出了自然变化空间，并表明变异配方均得到良好。我们分析了由于傅立叶截断而引起的误差，并得出结论，对于足够规律的数据，解决少数二维问题就足够了。
We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an equivalent, countable family of decoupled two-dimensional problems. By using decomposition of three-dimensional Sobolev norms we derive natural variational spaces for the two-dimensional problems, and show that the variational formulations are well-posed. We analyze the error due to Fourier truncation and conclude that, for data that are sufficiently regular, it suffices to solve a small number of two-dimensional problems.
