本篇學(xué)術(shù)論文我們主要研究分數(shù)次Navier-Stokes方程在變指標的臨界(?)里的柯西問題.首先,我們討論了變指標的Fourier-Besov空間的一些性質(zhì).我們得到分數(shù)次Navier-Stokes方程在變指標的Fourier-Besov空間上的全局適定性.除此之外,我們也證明了更一般旋轉(zhuǎn)Magneohydrodynamics方程在變指標的Fourier-Besov空間(?)的全局適定性,這個結(jié)果覆蓋了原有的結(jié)果.其次,我們考慮了Navier-Stokes方程在變指標Fourier-Besov-Morrey空間(?)with s(·)=4-2α-3/(p(·))上的柯西問題.得到分數(shù)次Navier-Stokes方程初值在(?)with s(.)=4-2α-3/(p(·))上充分小的全局適定性.

【文章頁數(shù)】：82 頁

【學(xué)位級別】：博士

【文章目錄】：
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



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