On the L2 decay of weak solutions for the 3D asymmetric fluids equations

Abstract

We study the long time behavior of weak solutions for the asymmetric fluids equations in the whole space R3. We prove that ‖(u,w)(⋅,t)‖L2(R3)2≤C(t+1)−3/2 for all t≥0 through Fourier splitting. Moreover, we use a direct method to show how to take advantage of the particular form of the equation for the angular velocity and obtain the so far unknown faster decay rate ‖w(⋅,t)‖L2(R3)2≤C(t+1)−5/2 for all t≥0.