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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
##### Keywords:
periodic boundary conditions; analytic Gevrey class
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##### References:
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