Geodesic
The optimal time decay rates for incompressible viscoelastic fluids in critical framework
Dandan Ding1 ; Meiling Chi1 ; Fuyi Xu1
1 School of Mathematics and Statistics Shandong University of Technology Shandong, China
Applicationes Mathematicae, Tome 47 (2020) no. 2, pp. 183-205.

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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.
DOI : 10.4064/am2409-5-2020
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

Dandan Ding 1 ; Meiling Chi 1 ; Fuyi Xu 1

1 School of Mathematics and Statistics Shandong University of Technology Shandong, China 
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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. http://geodesic.mathdoc.fr/articles/10.4064/am2409-5-2020/

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