Boussinesq方程组在Besov空间中局部解的存在性和延拓准则 |
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引用本文: | 原保全. Boussinesq方程组在Besov空间中局部解的存在性和延拓准则[J]. 数学学报, 2010, 53(3): 455-468 |
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作者姓名: | 原保全 |
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作者单位: | 河南理工大学数学与信息科学学院 焦作 454000 |
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基金项目: | 国家自然科学基金资助项目 (10771052);河南省创新型科技人才队伍建设工程;河南省高校科技创新人才支持计划 (2009HASTIT007)及河南理工大学博士基金 (B2008-62) |
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摘 要: | 本文研究二维无粘性Boussinesq方程组在超临界Besov空间B_(p,q)~s(R~2),s>1+2/p,1
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关 键 词: | Boussinesq方程组 Besov空间 存在性与唯一性 爆破准则 |
收稿时间: | 2008-03-25 |
修稿时间: | 2009-10-27 |
Local Existence and Continuity Conditions of Solutions to the Boussinesq Equations in Besov Spaces |
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Affiliation: | School of Mathematics and Informatics, He'nan Polytechnic University, He'nan Province, Jiaozuo 454000, P. R. China |
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Abstract: | In this paper, we study the 2D invisid Boussinesq equations, and prove the local existence and uniqueness of solutions in Besov space for super critical case s > 1 + 2/p, 1 < p < +∞, 1≤q≤+∞, and critical case s = 1 + 2/p with p∈(1,+∞) and q = 1. The blow-up criteria of the local solutions constructed are also obtained, which improves the Beale--Kato--Majda type criterion in homogeneous Besov space . Moreover, our blow-up criteria are only imposed on ∇θ. |
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Keywords: | Boussinesq equations Besov spaces existence and uniqueness blow-up criteria |
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