Recent Developments in the Navier-Stokes Problem
Recent Developments in the Navier-Stokes Problem
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DOI：
10.1201/9781420035674
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发表时间：
2002-04
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影响因子：
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通讯作者：
P. Lemarié–Rieusset
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文献类型：
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作者：
P. Lemarié–Rieusset
这本书是关于什么的？实调和分析的一些结果实插值，Lorentz空间，Sobolev嵌入Besov空间和Littlewood-Paley分解分布及相关Besov空间的平移不变Banach空间和Calderon-Zygmund算子向量值奇异积分小波入门小波与泛函空间空间BMO NAVIER-STOKES方程平移不变估计的一般框架NAVIER-STOKES方程的弱解无散度矢量小波缓和的NAVIER-STOKES方程的经典存在性结果NAVIER-STOKES方程的Leray解Kato NAVIER-STOKES方程的温和解新温和解的方法Koch和Tataru的温和解：Lp理论的空间BMO-1推广Navier-Stokes和局部测度的进一步结果局部测度正则初值负阶Besov空间负阶点乘子对Navier-Stokes方程的进一步适应空间Cannone的自相似衰减方法和弱、温和解的正则性结果Navier-Stokes方程的空间解析解空间局部化和Navier-Stokes方程的时间衰减；Navier-Stokes方程的解的惟一性；Ld解的唯一性R3上NAVIER-STOKES方程温和解的唯一性、稳定性和Lyapunov泛函局部能量不等式的进一步结果关于奇异点集维数的Nirenberg正则性准则局部适宜的局部平方可积弱解的局部存在性局部适宜的平方可积弱解的整体存在性Leray关于自相似奇点的猜想结论奇异初值
INTRODUCTION What is this Book About? SOME RESULTS OF REAL HARMONIC ANALYSIS Real Interpolation, Lorentz Spaces, and Sobolev Embedding Besov Spaces and Littlewood-Paley Decomposition Shift-Invariant Banach Spaces of Distributions and Related Besov Spaces Vector-Valued Integrals Complex Interpolation, Hardy Space, and Calderon-Zygmund Operators Vector-Valued Singular Integrals A Primer to Wavelets Wavelets and Functional Spaces The Space BMO A GENERAL FRAMEWORK FOR SHIFT-INVARIANT ESTIMATES FOR THE NAVIER-STOKES EQUATIONS Weak Solutions for the Navier-Stokes Equations Divergence-Free Vector Wavelets The Mollified Navier-Stokes Equations CLASSICAL EXISTENCE RESULTS FOR THE NAVIER-STOKES EQUATIONS The Leray Solutions for the Navier-Stokes Equations Kato's Mild Solutions for the Navier-Stokes Equations NEW APPROACHES OF MILD SOLUTIONS The Mild Solutions of Koch and Tataru: The Space BMO-1 Generalization of the Lp Theory: Navier-Stokes and Local Measures Further Results on Local Measures Regular Initial Values Besov Spaces of Negative Order Pointwise Multipliers of Negative Order Further Adapted Spaces for the Navier-Stokes Equations Cannone's Approach of Self-Similarity DECAY AND REGULARITY RESULTS FOR WEAK AND MILD SOLUTIONS Space-Analytic Solutions of the Navier-Stokes Equations Space Localization and Navier-Stokes Equations Time Decay for the Solutions to the Navier-Stokes Equations Uniqueness of Ld Solutions Further Results on Uniqueness of Mild Solutions Stability and Lyapunov Functionals LOCAL ENERGY INEQUALITIES FOR THE NAVIER-STOKES EQUATIONS ON R3 The Caffarelli, Kohn, and Nirenberg Regularity Criterion On the Dimension of the Set of Singular Points Local Existence (in Time) of Suitable Locally Square Integrable Weak Solutions Global Existence of Suitable Locally Square Integrable Weak Solutions Leray's Conjecture on Self-Similar Singularities CONCLUSION Singular Initial Values REFERENCES BIBLIOGRAPHY INDEX NOMINUM INDEX RERUM