Viscous flows in Besov spaces. (English) Zbl 0980.35125

Málek, Josef (ed.) et al., Advances in mathematical fluid mechanics. Lecture notes of the 6th international school on mathematical theory in fluid mechanics, Paseky, Czech Republic, September 19-26, 1999. Berlin: Springer. 1-34 (2000).
This is a survey of results of existence and uniqueness to the Navier-Stokes equations \[ \frac{\partial v}{\partial t}+(v\cdot\nabla)v-\nu\Delta v+\nabla p=f,\quad \text{div }v=0, \qquad v(x,0)=v_0(x). \] Results obtained in different functional spaces, especially in Besov spaces, are discussed. The time period of reviewed works runs from 1930 (pioneering papers of J. Leray) up to 2000 (R. Temam). The reader can find the references of many interesting but rarely cited works. Linguistic and philosophical excursions revive the text of the survey.
For the entire collection see [Zbl 0949.00020].


35Q30 Navier-Stokes equations
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
46N20 Applications of functional analysis to differential and integral equations