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

Abstract

We establish an asymptotic profile that sharply describes the behavior as $t\to \infty$ 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, e.g., in $L^3\_\mathrm{loc}(R^{+}\times R^3)$, provided $\epsilon \to 0$, where $\epsilon >0$ 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 $t\to +\infty$ than the corresponding solutions of Navier-Stokes.

Submitted to the Journal of the London Mathematical Society (under revision)

References in corpus (3)

• Decay characterization of solutions to dissipative equations
• Poincaré's inequality and diffusive evolution equations
• Espaces critiques pour le système des equations de Navier-Stokes incompressibles

Cited by in corpus (1)

• Forced Rapidly Dissipative Navier--Stokes Flows