Global Well-posedness of Fractioal Navier-Stokes Equations i

发布时间：2024-07-01 20:59

　　本篇学术论文我们主要研究分数次Navier-Stokes方程在变指标的临界(?)里的柯西问题.首先,我们讨论了变指标的Fourier-Besov空间的一些性质.我们得到分数次Navier-Stokes方程在变指标的Fourier-Besov空间上的全局适定性.除此之外,我们也证明了更一般旋转Magneohydrodynamics方程在变指标的Fourier-Besov空间(?)的全局适定性,这个结果覆盖了原有的结果.其次,我们考虑了Navier-Stokes方程在变指标Fourier-Besov-Morrey空间(?)with s(·)=4-2α-3/(p(·))上的柯西问题.得到分数次Navier-Stokes方程初值在(?)with s(.)=4-2α-3/(p(·))上充分小的全局适定性.

【文章页数】：82 页

【学位级别】：博士

【文章目录】：
Abstract
摘要
1 Introduction
    1.1 Nonlinear Evolution Equations
        1.1.1 Navier-Stokes Equations
    1.2 Well-posed problem
        1.2.1 Locally well-posed and Globally well-posed
    1.3 Banach contraction principle
    1.4 Littlewood-Paley Decomposition
        1.4.1 Besov spaces
        1.4.2 Homogeneous Besov spaces
        1.4.3 Some important properties of Besov spaces
    1.5 Paradifferential Calculus
    1.6 Outline of the thesis
    1.7 Basic Notations and Definitions
2 Besov Spaces with variable
    2.1 Background
    2.2 Preliminaries
3 Global well-posedness of fracrtional Navier-Stokes equations
    3.1 The fractional Navier-Stokes equations
        3.1.1 Equivalent form of (FNS) equations
    3.2 Main result
4 Global well-posedness of the Generalized Rotating Magnetohydro-dynamics Equations
    4.1 Introduction and Mathematical Backgroung
    4.2 Global well-posedness of the Generalized Rotating MHD Equations
5 Morrey spaces with variable exponent
    5.1 Introduction
        5.1.1 Morrey spaces with varaible exponent
    5.2 Preliminaries
        5.2.1 Some important lemmas
        5.2.2 Homogeneous Besov-Morrey spaces with variable exponents
        5.2.3 Homogeneous Fourier-Besov-Morrey spaces with variable expo-nents
6 Global well-posedness of fracrtional Navier-Stokes equation in vari-able exponent Fourier-Besov-Morrey spaces
    6.1 Some important propositions
    6.2 The global well-posedness of the fractional Navier-Stokes equations
Bibliography
Papers published
Acknowledgement



本文编号：3999175