The Incompressible Navier–Stokes Equations on Non-compact Manifolds

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• 作者：Vittoria Pierfelice
• 关键词：Navier–Stokes equations ; Non ; compact Riemannian manifolds ; Hyperbolic space ; Bochner Laplacian ; Dispersive estimates ; Smoothing estimates
• 刊名：The Journal of Geometric Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：27
• 期：1
• 页码：577-617
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Differential Geometry; Convex and Discrete Geometry; Fourier Analysis; Abstract Harmonic Analysis; Dynamical Systems and Ergodic Theory; Global Analysis and Analysis on Manifolds;
• 出版者：Springer US
• ISSN：1559-002X
• 卷排序：27

文摘

We shall prove dispersive and smoothing estimates for vectorial heat equations associated with Bochner type Laplacians on some non-compact Riemannian manifolds with negative Ricci curvature, in particular on hyperbolic spaces. The negative curvature yields better large time decay than in the Euclidean case. Besides their own known interest in harmonic analysis, these estimates will be used to prove Fujita–Kato type theorems for the incompressible Navier–Stokes equations. We shall also discuss the uniqueness of Leray weak solutions in the two-dimensional case.