Global Weak Solutions to Non-isothermal Nematic Liquid Crystals in 2D

摘要: In this paper, we prove the global existence of weak solutions to non-isothermal nematic liquid crystal system on $\mathbb T^2$, based a new approximate which is different from classical Ginzburg-Landau approximation. Local energy inequalities are employed recover estimates second order spacial derivatives director fields locally in time, cannot be derived basic balance. It shown that these conserve total and while kinetic potential energies transfer heat precisely. Furthermore, it also established have at most finite many singular times concentration occurs, as result, temperature must increase suddenly each time some part T^2$.