# zbMATH — the first resource for mathematics

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.

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