【摘要】 该文研究了用简化的Ginzburg-Landau模型刻画的不可压液晶方程组的解的适定性问题,该模型是目前为止保持不可压液晶方程的非线性性质的最简单的模型（参见文献[1]）.该文得到了在初始资料满足以下条件u₀∈L^p ∩ H,d₀∈W^1,p,p≥n时,不可压液晶方程组的解具有存在唯一性.根据文献[2]中不可压液晶方程组的解的正则性的Serrin判定准则,该文得到了小初值光滑解的整体存在性和大初值光滑解的局部存在性.更多还原

【Abstract】 In this paper,we study the nematic liquid crystals system under the simplified Ginzburg-Landau model,which is probably the simplest mathematical model that one can derive,without destroying the basic nonlinear structure [1].We get the local existence and uniquness of the Serrin’s type of solutions provided the initial data u₀∈L^p∩ H,and d₀∈W^1,p,p≥ n.According to the Serrin’s regularity criteria for the incompressible liquid crystals system [2],we actually prove the local existence of smooth solutions to liquid crystals system for big data and global existence of smooth solutions for small data.更多还原