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

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 t...

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Bibliographic Details
Published in:Journal of Differential Equations 2019-09, Vol.267 (6), p.3578-3609
Main Authors: Braz e Silva, P., Cruz, F.W., Freitas, L.B.S., Zingano, P.R.
Format: Article
Language:English
Subjects:
Asymmetric fluids
Decay rates
Fourier splitting
Weak solutions
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2019.04.012