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| Remark on the Regularities of Kato’sSolutions to Navier-Stokes Equations with Initial Data in L^d(R^d) |
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Citation： |
Ping ZHANG.Remark on the Regularities of Kato’sSolutions to Navier-Stokes Equations with Initial Data in L^d(R^d)[J].Chinese Annals of Mathematics B,2008,29(3):265~272 |
| Page view： 1010
Net amount： 875 |
Authors： |
Ping ZHANG; |
Foundation： |
Project supported by the National Natural Science Foundation of China (Nos. 10525101, 10421101), the
973 Project of the Ministry of Science and Technology of China and the innovation grant from Chinese Academy of Sciences. |
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| Abstract： |
Motivated by the results of J. Y. Chemin in “J. Anal. Math., 77, 1999, 27–50” and G. Furioli et al in “Revista Mat.Iberoamer., 16, 2002, 605–667”, the author considers further regularities of the mild solutions to Navier-Stokes equation with initial data u^0 \in L^d(R^d). In particular, it is proved that if u\in C([0,T^\ast);L^d(\R^d)) is a mild
solution of (NS_\nu), then u(t,x)-\ee^{\nu t\D}u_0 \in\tL^\infty((0,T);\dot{B}^{1}_{\frac{d}2,\infty})\cap\tL^1((0,T);\dot{B}^{3}_{\frac{d}2,\infty}) for any T |
Keywords： |
Navier-Stokes equations, Kato’s solutions, Para-differential decomposition |
Classification： |
35L60, 76A02 |
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