Global existence of weak solutions to the non-isothermal nematic liquid crystals in 2D
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- 作者：Jinkai LIa ; b ; jklimath@gmail.com" class="auth_mail" title="E-mail the corresponding author ; Zhouping XINc ; zpxin@ims.cuhk.edu.hk" class="auth_mail" title="E-mail the corresponding author
- 关键词：Global weak solutions ; non-isothermal ; nematic liquid crystals
- 刊名：Acta Mathematica Scientia
- 出版年：2016
- 出版时间：July 2016
- 年：2016
- 卷：36
- 期：4
- 页码：973-1014
- 全文大小：444 K
文摘
In this article, we prove the global existence of weak solutions to the non-isothermal nematic liquid crystal system on 
2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many “singular” times, at which the energy concentration occurs and the director field losses its second order derivatives.
2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many “singular” times, at which the energy concentration occurs and the director field losses its second order derivatives.