兰州大学机构库 >数学与统计学院
3D 薄区域上具有Navier-摩擦边界条件的Navier-Stokes方程的全局强解和吸引子的存在性
其他题名The existences of global strong solution and of attractor for Navier-Stokes equations in 3D thin domains with Navier-friction boundary conditions
刘辉
导师钟承奎
学位类别硕士
2008-05-26
关键词Navier Stokes 方程 3D 薄区域 Navier 摩擦边界条件 吸引子
中文摘要在这篇硕士学位论文中, 我们考虑三维薄区域上的 Navier-Stokes方程的强解的全局存在性和吸引子的存在性,区域上的上边界不是平的。我们考虑如下的边界条件: ``在区域上的水平方向上是周期边界条件, 在区域上的垂直方向上是一般的 Navier 摩擦边界条件"。假设初始条件外力项满足适当的条件下,我们证明了方程的强解的全局存在性,假设 f 在 L^\infty(0,~\infty; L^(\Omega_\varepsilon)^3) 中是平移紧的,使用在[24]中方法, 我们证明了三维Navier-Stokes方程强解局部吸引子的存在性。
英文摘要In this master thesis, we consider the solutions of Navier-Stokes equations on thin 3D domains where the top boundary is non-flat. We consider the following boundary conditions:`` periodic boundary conditions on the lateral boundary and general{Navier-friction boundary conditions}on the top and the bottom boundary". similar assumptions on the forcing term, we show global existence of strong solutions, hereUnder the assumption that f is translation compact in L^\infty(0,~\infty; L^(\Omega_\varepsilon)^3), by using the method in [24], we show the existence of (local) attractor of strong solutions for 3D Navier-Stokes equations.
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授予单位兰州大学
授予地点兰州
语种中文
文献类型学位论文
条目标识符http://ir.lzu.edu.cn/handle/262010/225747
Collection数学与统计学院
Recommended Citation:
GB/T 7714
刘辉. 3D 薄区域上具有Navier-摩擦边界条件的Navier-Stokes方程的全局强解和吸引子的存在性[D]. 兰州. 兰州大学,2008.
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