On $$L^2$$ decay of weak solutions of several incompressible fluid models

Abstract

In this paper, we are concerned with \(L^2\) decay of weak solutions of several well-known incompressible fluid models, such as the n-dimensional (\(n\ge 2\)) Navier–Stokes equations with fractional hyperviscosity, the three-dimensional convective Brinkman–Forchheimer equations and the generalized SQG equation. A new approach, different from the classical Fourier splitting method develpoed by Schonbek (Commun Partial Differ Equ 11:733–763, 1986) and the spectral representation technique by Kajikiya and Miyakawa (Math Z 192:135-148,1986), is presented. By using the new approach, we can recover and improve some known decay results.