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
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[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
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