Ciprian Foias
University of Paris-Sud
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Directions in Partial Differential Equations#R##N#Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 28–30, 1985 | 1987
Ciprian Foias; Roger Temam
Publisher Summary There are three major distinct but not mutually contradictory theoretical views on turbulence—(a) the statistical view, in which the turbulence is considered as the observed behavior of the evolution of statistical distributions of flows instead of the evolution of one individual flow; (b) the viewpoint of regularity breakdown, in which the turbulence is considered to result from the blow-up of the vorticity in finite time, albeit necessarily on a set of small Hausdorff dimension; and (c) the dynamical systems view, in which the turbulence is a phenomenologic perception of the long time complicated behavior of the individual flows. The chapter discusses that it is reasonable to test them by trying to establish rigorous mathematical facts based on the Navier–Stokes equations, the interpretation of which are consistent with any of the three viewpoints mentioned above. The chapter presents the contribution by Ciprian Foias and Roger Temam to this program from the dynamical systems point of view. The chapter presents a proof of a regularity and backward uniqueness theorem on an open dense subset of the universal attractor of the 3D Navier–Stokes equations.
North-holland Mathematics Studies | 1982
Ciprian Foias; Roger Temam
Publisher Summary This chapter discusses finite parameter approximative structure of actual flows. To explain the concept, it considers the Navier–Stokes equations, which are Galilean invariant.
Communications in Partial Differential Equations | 1981
Ciprian Foias; Colette Guillopé; Roger Temam
Journal of Differential Equations | 1985
Ciprian Foias; Colette Guillopé; Roger Temam
Archive | 1975
Ciprian Foias; Roger Temam
Archive | 2001
Ciprian Foias; Oscar P. Manley; Ricardo Rosa; Roger Temam
Archive | 2010
Ciprian Foias; Ricardo Rosa
Archive | 1990
Ciprian Foias; Roger Temam
Archive | 1989
Basil Nicolaenko; Ciprian Foias; Roger Temam
Archive | 1989
Peter Constantin; Ciprian Foias; Basil Nicolaenko; Roger Temam