On a non-solenoidal approximation to the incompressible Navier-Stokes equations

Abstract

We establish an asymptotic profile that sharply describes the behavior as t→∞ for solutions to a non‐solenoidal approximation of the incompressible Navier–Stokes equations introduced by Temam. The solutions of Temam's model are known to converge to the corresponding solutions of the classical Navier–Stokes, for example, in L loc 3false(double-struckR+×double-struckR3false), provided ε→0, where ε>0 is the physical parameter related to the artificial compressibility term. However, we show that such model is no longer a good approximation of Navier–Stokes for large times: indeed, its solutions can decay much slower as t→∞ than the corresponding solutions of Navier–Stokes.

Asymptotic behavior of solutions to incompressible electron inertial Hall-MHD system in $ \mathbb{R}^3 $

“…There are some other papers studied the decay characterization of dissipative equations (cf. [23,9,5,32,34] and the reference therein). For more details on P r and r * , we refer to Section 2.…”