| 二维quasi-geostrophic方程的几何结构和非爆炸性 |
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| 引用本文： | 邓健,纪冕. 二维quasi-geostrophic方程的几何结构和非爆炸性[J]. 复旦学报(自然科学版), 2008, 47(2): 224-231 |
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| 作者姓名： | 邓健 纪冕 |
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| 作者单位： | 复旦大学,数学科学学院,上海,200433 |
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| 摘 要： | 讨论了二维quasi-geostrophic方程中的主动标量θ的封闭水平集C的动态演变.当水平集具有某种指定几何性质,那么在水平集上▽⊥θ的大小与Ω(t)可比的假设下,证明了有限时间T内解爆炸的不存在性.最后给出了一个2D QG方程的Lax对表示.
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| 关 键 词： | 二维quasi-geostrophic方程 Lax对 有限时间爆炸 |
| 文章编号： | 0427-7104(2008)02-0224-08 |
| 修稿时间： | 2006-11-23 |
Geometric Structure and Non-blowup of 2DQuasi-geostrophic Equation |
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| DENG Jian,JI Mian. Geometric Structure and Non-blowup of 2DQuasi-geostrophic Equation[J]. Journal of Fudan University(Natural Science), 2008, 47(2): 224-231 |
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| Authors: | DENG Jian JI Mian |
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| Abstract: | The dynamic evolution of a closed level set C of active scalar θ in the 2D quasi-geostrophic equation is studied. Under some mild assumptions about the geometry of the level set and with the condition that the magnitude of ⊥θ along C is comparable to Ω(t), it is shown that there is no finite-time blowup up to time T. Later, in order to further analyze 2D QG equation, a Lax pair representation (L,A) of the equation is discussed. |
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| Keywords: | 2D quasi-geostrophic equation Lax pair finite-time blowup |
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