The optimal time decay rates for incompressible viscoelastic fluids in critical framework
Applicationes Mathematicae, Tome 47 (2020) no. 2, pp. 183-205
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We study the Cauchy problem for multi-dimensional incompressible viscoelastic fluids in the whole space. The optimal time decay rates of strong solution constructed by Qian (2010), and Zhang (2011) in $L^{2}$-critical regularity framework are obtained for low frequencies of the data under a suitable additional condition. The proof relies on an application of Fourier analysis to a mixed parabolic-hyperbolic system, and on a refined time-weighted energy functional. As a by-product, time decay rates of $L^{q}$-$L^{r}$ type are also captured in the critical framework.
Keywords:
study cauchy problem multi dimensional incompressible viscoelastic fluids whole space optimal time decay rates strong solution constructed qian zhang critical regularity framework obtained low frequencies under suitable additional condition proof relies application fourier analysis mixed parabolic hyperbolic system refined time weighted energy functional by product time decay rates l type captured critical framework
Affiliations des auteurs :
Dandan Ding 1 ; Meiling Chi 1 ; Fuyi Xu 1
@article{10_4064_am2409_5_2020,
author = {Dandan Ding and Meiling Chi and Fuyi Xu},
title = {The optimal time decay rates for incompressible viscoelastic fluids in critical framework},
journal = {Applicationes Mathematicae},
pages = {183--205},
year = {2020},
volume = {47},
number = {2},
doi = {10.4064/am2409-5-2020},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am2409-5-2020/}
}
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Dandan Ding; Meiling Chi; Fuyi Xu. The optimal time decay rates for incompressible viscoelastic fluids in critical framework. Applicationes Mathematicae, Tome 47 (2020) no. 2, pp. 183-205. doi: 10.4064/am2409-5-2020
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