Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Note on Stokes Approximations to Leray Solutions of the Incompressible Navier-Stokes Equations in Rn

Version 1 : Received: 29 July 2021 / Approved: 2 August 2021 / Online: 2 August 2021 (11:47:33 CEST)

A peer-reviewed article of this Preprint also exists.

Rigelo, J.C.; Zingano, J.P.; Zingano, P.R. A Note on Stokes Approximations to Leray Solutions of the Incompressible Navier–Stokes Equations in ℝn. Fluids 2021, 6, 340. Rigelo, J.C.; Zingano, J.P.; Zingano, P.R. A Note on Stokes Approximations to Leray Solutions of the Incompressible Navier–Stokes Equations in ℝn. Fluids 2021, 6, 340.

Journal reference: Fluids 2021, 6, 340
DOI: 10.3390/fluids6100340

Abstract

In the early 1980s it was well established that Leray solutions of the unforced Navier-Stokes equations in Rn decay in energy norm for large time. With the works of T. Miyakawa, M. Schonbek and others it is now known that the energy decay rate cannot in general be any faster than t^-(n+2)/4 and is typically much slower. In contrast, we show in this note that, given an arbitrary Leray solution u(.,t), the difference of any two Stokes approximations to the Navier-Stokes flow u(.,t) will always decay at least as fast as t^-(n+2)/4, no matter how slow the decay of || u(.,t) ||_L2 might happen to be.

Keywords

Navier-Stokes equations, Stokes flows, Leray solutions, large time behavior

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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