| 可压缩液晶系统强解的破裂准则 |
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| 引用本文： | 刘兰明,刘宪高.可压缩液晶系统强解的破裂准则[J].数学年刊A辑(中文版),2011,32(4):393-406. |
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| 作者姓名： | 刘兰明 刘宪高 |
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| 作者单位： | 复旦大学数学科学学院; |
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| 基金项目： | 国家自然科学基金(No11071043)资助的项目 |
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| 摘 要： | 研究可压缩液晶方程组强解的破裂准则,建立了一种仅依据于速度梯度的破裂准则,此种准则类似于理想可压缩流情形的Beale-Kato-Majda准则和由Huang和Xin得到的可压缩Navier-Stokes方程组情形的准则.证明用到能量不等式和高阶能量不等式.主要困难是初始密度含有真空.
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| 关 键 词： | 破裂准则 强解 液晶方程 可压缩Navier-Stokes方程组 |
A Blow-up Criterion of Strong Solutions to the Compressible Liquid Crystals System |
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| LIU Lanming and LIU Xiangao.A Blow-up Criterion of Strong Solutions to the Compressible Liquid Crystals System[J].Chinese Annals of Mathematics,2011,32(4):393-406. |
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| Authors: | LIU Lanming and LIU Xiangao |
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| Institution: | LIU Lanming~1 LIU Xiangao~1 1 School of Mathematical Sciences,Fudan University,Shanghai 200433,China. |
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| Abstract: | The authors establish a blow-up criterion of the strong solutions to the compressible liquid crystals equations in terms of the gradient of the velocity only,similar to Beale-Kato-Majda criterion for the ideal incompressible flows and the criterion obtained by Huang and Xin for the compressible Navier-Stokes equations.The energy law and a higher order energy inequality will be employed to prove this criterion.The main difficulty comes from the vacuum at the initial time. |
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| Keywords: | Blow-up criterion Strong solutions Liquid crystals equations Compressible Navier-Stokes equations |
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