Littlewood-Paley decomposition and Navier-Stokes equations. (English) Zbl 0842.35074

The authors prove some existence and uniqueness results for the local strong solutions of the Cauchy problem for the Navier-Stokes equations in \( \mathbb{R}^3\). They are primarily interested in strong solutions belonging to \(C([0,T); X)\), where \(X\) denotes an abstract Banach space of vector distributions on \(\mathbb{R}^3\). In contrast to earlier work in which the spaces were adapted to specific methods, the authors present a general approach which can be used for a variety of Banach spaces satisfying a simple sufficient condition. Examples are given. The analysis is partly inspired by the wavelet approach of Federbush, and it rests upon a systematic use of the Littlewood-Paley decomposition.


35Q30 Navier-Stokes equations
42B25 Maximal functions, Littlewood-Paley theory
Full Text: DOI