zbMATH — the first resource for mathematics

Gevrey class regularity for the solutions of the Navier-Stokes equations. (English) Zbl 0702.35203
Let u(t,x), for \(0\leq t\leq t_ 0\), \(x\in [0,L]^ d\) \((d=2\) or 3), be a regular solution of the Navier-Stokes equations with periodic boundary conditions and potential forces and let A be the corresponding Stokes operator. Then for \(t>0\) as function of x, u(t,x) belongs to an analytic Gevrey class. In particular, for \(t>0\) but small enough, u(t,\(\cdot)\) is in the domain of the operator \(\exp (tA^{1/2})\).
Reviewer: C.Foias

35Q30 Navier-Stokes equations
35B65 Smoothness and regularity of solutions to PDEs
Full Text: DOI
[1] Foias, C; Manley, O; Temam, R; Foias, C; Manley, O; Temam, R, Modélisation of the interaction of small and large eddies in turbulent flows, C. R. acad. sci. Paris Sér. I math., math. mod. num. anal. (M2AN), 22, 93-114, (1988) · Zbl 0663.76054
[2] Foias, C; Temam, R, On the stationary statistical solutions of the Navier-Stokes equations and turbulence, () · Zbl 0702.35203
[3] Foias, C; Temam, R, Some analytic and geometric properties of the solutions of the Navier-Stokes equations, J. math. pures appl., 58, 339-368, (1979) · Zbl 0454.35073
[4] Lions, J.L, Quelques méthodes de résolution des problèmes aux limites non linéaires, (1969), Dunod Paris · Zbl 0189.40603
[5] Masuda, K, On the analyticity and the unique continuation theorem for solutions of the Navier-Stokes equations, (), 827-832, No. 9 · Zbl 0204.26901
[6] Temam, R, Navier-Stokes equations and nonlinear functional analysis, () · Zbl 0833.35110
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.