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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数学学报 ›› 2010, Vol. 53 ›› Issue (3) : 455-468.

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数学学报 ›› 2010, Vol. 53 ›› Issue (3) : 455-468. DOI: 10.12386/A2010sxxb0051
论文

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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Local Existence and Continuity Conditions of Solutions to the Boussinesq Equations in Besov Spaces

    Bao Quan YUAN
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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,s>1+2/p, 1<p<+∞, 1≤q≤+∞和临界Besov空间, p∈(1,+∞)局部解的存在性和唯一性, 并且得到了局部解仅使用∇θ的爆破准则, 该准则将Beale--Kato--Majda型准则推广到了齐次Besov空间.  

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.  

关键词

Boussinesq方程组 / Besov空间 / 存在性与唯一性 / 爆破准则

Key words

Boussinesq equations / Besov spaces / existence and uniqueness / blow-up criteria

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原保全. Boussinesq方程组在Besov空间中局部解的存在性和延拓准则. 数学学报, 2010, 53(3): 455-468 https://doi.org/10.12386/A2010sxxb0051
Bao Quan YUAN. Local Existence and Continuity Conditions of Solutions to the Boussinesq Equations in Besov Spaces. Acta Mathematica Sinica, Chinese Series, 2010, 53(3): 455-468 https://doi.org/10.12386/A2010sxxb0051

参考文献



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基金

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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