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Abstract: We consider the incompressible Navier-Stokes NS equations on a torus, inthe setting of the spaces L^2 and H^1; our approach is based on a generalframework for semi- or quasi-linear parabolic equations proposed in theprevious work 9. We present some estimates on the linear semigroup generatedby the Laplacian and on the quadratic NS nonlinearity; these are fullyquantitative, i.e., all the constants appearing therein are given explicitly.As an application we show that, on a three dimensional torus T^3, the mildsolution of the NS Cauchy problem is global for each H^1 initial datum u 0 withzero mean, such that || curl u 0 || {L^2} <= 0.407; this improves the bound forglobal existence || curl u 0 || {L^2} <= 0.00724, derived recently by Robinsonand Sadowski 10. We announce some future applications, based again on the H^1framework and on the general scheme of 9.



Autor: Carlo Morosi Politecnico di Milano, Livio Pizzocchero Universita' di Milano

Fuente: https://arxiv.org/



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