| 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,2011,32(4):393~406 |
| 可压缩液晶系统强解的破裂准则 |
| A Blow-up Criterion of Strong Solutions to the Compressible Liquid Crystals System |
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| DOI： |
| 中文关键词: 破裂准则 强解 液晶方程 可压缩Navier-Stokes方程组 |
| 英文关键词:Blow-up criterion Strong solutions Liquid crystals equations Compressible Navier-Stokes equations |
| 基金项目:国家自然科学基金(No11071043)资助的项目 |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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