On the decay and Gevrey regularity of the solutions to the Navier–Stokes equations in general two-dimensional domains

The present paper is devoted to the proof of time decay estimates for derivatives at any order of finite energy global solutions of the Navier–Stokes equations in general two-dimensional domains. These estimates only depend on the order of derivation and on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> norm of the initial data. The same elementary method just based on energy estimates and Ladyzhenskaya inequality also leads to Gevrey regularity results.