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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

MSC:
35Q30 Navier-Stokes equations
35B65 Smoothness and regularity of solutions to PDEs
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