| Quasi-Geostrophic方程经典解的爆破准则 |
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| 引用本文： | 崔文会.Quasi-Geostrophic方程经典解的爆破准则[J].吉首大学学报(自然科学版),2012,33(2):19-23. |
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| 作者姓名： | 崔文会 |
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| 作者单位： | （湘潭大学数学与计算机科学学院，湖南 湘潭 411105） |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 考虑Quasi-Geostrophic方程,以经典解沿流线小时间的表现,给出Quasi-Geostrophic方程经典解沿流线爆破的一个充分条件.方法是从Quasi-Geostrophic方程推出一个解的梯度长度的倒数沿流线的微分不等式,从而推出结论.手法与结果都类似于Chae关于3维不可压Euler方程组经典解的爆破工作.该结果对进一步研究Quasi-Geostrophic方程相关问题,有一定的启示作用.
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| 关 键 词： | Quasi-Geostrophic方程 经典解 爆破准则 |
Blow-up Criterion of Classical Solution of Quasi-Geostrophic Equation |
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| CUI Wen-hui.Blow-up Criterion of Classical Solution of Quasi-Geostrophic Equation[J].Journal of Jishou University(Natural Science Edition),2012,33(2):19-23. |
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| Authors: | CUI Wen-hui |
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| Institution: | (School of Mathematics and Computational Sciences,Xiangtan University,Xiangtan 411105,Hunan China) |
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| Abstract: | The quasi-geostrophic equation is considered in this paper.A criterion is given for the finite time blow-up of a classical solution in terms of its small time behaviors along the trajectories.The result is deduced from a differential inequality for the reciprocal of the length of the gradient of the solution along a particle trajectories.The method and the result are similar to those of Chae on the 3 dimensional incompressible Euler system.The result gives some inspiration for the further research of quasi-geostrophic equation. |
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| Keywords: | Quasi-Geostrophic equation classical solution blow-up criterion |
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