Local existence and blow‐up criterion for the generalized Boussinesq equations in Besov spaces |
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| Authors: | Hua Qiu Yi Du Zheng'an Yao |
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| Institution: | 1. Department of Applied Mathematics, South China Agricultural University, , Guangzhou, 510642 China;2. School of Mathematical Sciences, South China Normal University, , Guangzhou, 510631 China;3. School of Mathematics and Computational Science, Sun Yat‐Sen University, , Guangzhou, 510275 China |
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| Abstract: | In this paper, we consider the three‐dimensional generalized Boussinesq equations, a system of equations resulting from replacing the Laplacian ? Δ in the usual Boussinesq equations by a fractional Laplacian ( ? Δ)α. We prove the local existence in time and obtain a regularity criterion of solution for the generalized Boussinesq equations by means of the Littlewood–Paley theory and Bony's paradifferential calculus. The results in this paper can be regarded as an extension to the Serrin‐type criteria for Navier–Stokes equations and magnetohydrodynamics equations, respectively. Copyright © 2012 John Wiley & Sons, Ltd. |
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| Keywords: | generalized Boussinesq equations regularity criterion local existence Littlewood– Paley decomposition |
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