We discuss the "transfer of regularity" phenomenon for the incompressible Navier--Stokes Equations (NSE) in dimension $n \geq 3$; that is, the strong solutions of NSE on $\mathbb{R}^n$ can be nicely approximated by those on sufficiently large domains $\Omega \subset \mathbb{R}^n$ under the no-slip boundary condition. Based on the spacetime decay estimates for mild solutions of NSE established by Miyakawa and Schonbek, etc., we obtain quantitative estimates on higher-order derivatives of velocity and pressure for the incompressible Navier--Stokes flow on large domains under certain additional smallness assumptions of the Stokes' system and/or the initial velocity, thus complementing the transfer of regularity theorems obtained by Robinson (Nonlinearity 2021) and O\.z\'anski (J. Math. Fluid Mech. 2021).
Joint work with Xiangxiang Su.
