Abstract
This paper is dedicated to investigating \(L^2\) time decay of the strong solution for the 2D Oldroyd-B model with linear stress tensor. Based on energy methods and new observation on the structure of the equations, we obtain the more rapid \(L^2\) decay rates of the strong solutions for the Oldroyd-B model as \(\Vert u(t)\Vert _{L^2} \le C(1+t)^{-1},\) \(\Vert \tau (t)\Vert _{L^2} \le C(1+t)^{-\frac{3}{2}}\) and \(\Vert \nabla u\Vert _{L^2}+\Vert \nabla \tau \Vert _{L^2}\le C(1+t)^{-\frac{3}{2}}\).
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Acknowledgements
The authors want to express their sincere thanks to the editors and the referees for their invaluable comments and suggestions which helped improve the paper greatly. Appreciation is also given to Professor Bo-Qing Dong for many helpful suggestion. Jia was supported by the NNSFC Grants (Nos.12001004, 11801002) and the NSF of Anhui Province (No. 2108085QA12).
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Feng, J., Jia, Y. & Wang, M. \(L^2\) Decay for the 2-D Oldroyd-B Model with Linear Damping Stress. Bull. Malays. Math. Sci. Soc. 47, 36 (2024). https://doi.org/10.1007/s40840-023-01635-7
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DOI: https://doi.org/10.1007/s40840-023-01635-7