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Asymptotic behavior for the Navier-Stokes equations with nonzero external forces |
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| Authors: | Hyeong-Ohk Bae Lorenzo Brandolese |
| Affiliation: | a Department of Mathematics, Ajou Univ., 443-749 Suwon, Republic of Korea b Université de Lyon, Université Lyon 1, Institut Camille Jordan, CNRS UMR 5208 43 bd. du 11 novembre 1918, 69622 Villeurbanne Cedex, France c Department of Mathematics, Mokpo Nat. Univ. Mokpo, Republic of Korea |
| Abstract: | We estimate the asymptotic behavior for the Stokes solutions, with external forces first. We found that if there are external forces, then the energy decays slowly even if the forces decay quickly. Then, we also obtain the asymptotic behavior in the temporal-spatial direction for weak solutions of the Navier-Stokes equations. We also provide a simple example of external forces which shows that the Stokes solution does not decay quickly. |
| Keywords: | 35Q30 76D05 76D07 |
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