兰州大学机构库 >数学与统计学院
非自治的二维Navier-Stokes 方程的一致吸引子
Alternative Titleuniform attractors for nonautonomous 2D Navier-Stokes equations
卢松松
Thesis Advisor钟承奎
2005-05-12
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
Keyword一致吸引子 Navier-Stokes 方程 过程 正规函数
Abstract本文考虑粘性不可压缩流体的非自治的二维Navier-Stokes 方程的解的长时间行为. 证明了具有新的一类外力项的此方程的一致吸引子的存在性及其结构. 这类外力项称为是正规的. 注意到, 正规函数类和平移紧函数类都是平移有界函数空间的闭子空间, 但平移紧函数类是正规函数类的真子集. 为此, 建立了一些抽象的结果. 首先, 应用非紧性测度的概念刻划了过程族的一致吸引子的存在性并提供了验证方法. 其次, 通过在赋予弱拓扑的相空间中构造斜积流来得到一致吸引子的结构. 其三, 证明过程的一致吸引子与具由初始符号的平移族在相对应的某个Banach 空间的取弱闭包得到的符号空间的过程族的一致吸引子是相同的. 最后, 估计了H 中的一致吸引子的核截片的分形维数. 本文的工作首次表明, 在不丢失原有性质的前提下, 由非平移强紧符号可以得到强紧的一致吸引子.
Other AbstractWe consider the long time behavior of the nonautonomous 2D Navier-stokes equations of viscous incompressible fluid. The existence and structure of uniform attractors is proved for the equations with a new class of external forces, termed normal. Note that the classes of the normal functions and translation compact functions are closed subspaces of the class of translation bounded functions but the latter is a proper subset of the former. To this end, some abstract results are established. First, a characterization on the existence of uniform attractor for a family of processes is presented by the concept of measure of noncompactness as well as methods to verify it. Second, the structure of the uniform attractor is obtained by constructing skew product flow on the extended phase space with weak topology. Third, the uniform attractor of a process is identified with that of a family of processes with symbols in the closure of the translation family of the original symbol in a Banach space with weak topology. Finally, the fractal dimension of the kernel section of the uniform attractor in H is estimated. This paper shows that it is possible to obtain the strongly compact uniform attractors preserving the principle properties for the systems with symbols that is not translation strongly compact.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225442
Collection数学与统计学院
Recommended Citation
GB/T 7714
卢松松. 非自治的二维Navier-Stokes 方程的一致吸引子[D]. 兰州. 兰州大学,2005.
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