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.
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