| 三维Euler方程的几何性质与非爆炸性的研究 |
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| 引用本文： | 靳鲲鹏,刘三明.三维Euler方程的几何性质与非爆炸性的研究[J].烟台大学学报(自然科学与工程版),2011,24(3). |
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| 作者姓名： | 靳鲲鹏 刘三明 |
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| 作者单位： | 上海电机学院数理研究所,上海,200240 |
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| 基金项目： | 上海市自然科学基金资助项目，上海市教委创新项目资助，上海市高校选拔培养优秀青年教师科研专项基金项目 |
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| 摘 要： | 利用水平集的几何性质和其上涡度之间的关系,研究三维不可压缩Euler方程组在有限时间内是否爆炸这一问题.假设涡线上涡度最大值与全局涡度最大值可比,运用涡度达到无穷大只是三维不可压缩Euler方程发生爆炸的必要条件而非充分条件这一思想,得到三维不可压缩Euler方程在有限时间内不会发生爆炸的结论.并重新估计了非爆炸性的条件,将原有定理中无爆炸发生的条件A+B≤1放宽到A+B＜2.
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| 关 键 词： | Euler方程 水平集 几何性质 非爆炸性 |
Geometric Properties and Non-blowup of 3D Euler Equation |
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| JIN Kun-peng,LIU San-ming.Geometric Properties and Non-blowup of 3D Euler Equation[J].Journal of Yantai University(Natural Science and Engineering edirion),2011,24(3). |
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| Authors: | JIN Kun-peng LIU San-ming |
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| Institution: | JIN Kun-peng,LIU San-ming(Institute of Applied Mathematics and Physics,Shanghai Dianji University,Shanghai 200240,China) |
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| Abstract: | Using the relations between the geometric properties of the level set and vorticity,we study the problem that the 3-D incompressible Euler equations blow up or not in finite time.As we all know,the infinity of vorticity is necessary but non-sufficient condition under which the 3-D incompressible Euler equations blow up.Suppose the maximum vorticity along this closed vortex line is comparable with the global maximum vorticity,the 3-D incompressible Euler equations can not blow up in finite time.Moreover,we g... |
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| Keywords: | Euler equations level set geometric properties non-blowup |
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