本文的主要目的在于提高三维可压缩向列型液晶系统解的最高阶(S阶)空间导数的衰减率。如果初值的HS(S≥3)和范数都是有界的,并且其H3范数足够小,则应用纯能量法,我们给出了解的最高阶空间导数L2范数的最优衰减率为(1+t)−(S2+α2),而在魏...本文的主要目的在于提高三维可压缩向列型液晶系统解的最高阶(S阶)空间导数的衰减率。如果初值的HS(S≥3)和范数都是有界的,并且其H3范数足够小,则应用纯能量法,我们给出了解的最高阶空间导数L2范数的最优衰减率为(1+t)−(S2+α2),而在魏,李和姚的研究中其衰减率仅为(1+t)−(S−12+α2)。Abstract: The major objective of this thesis lies in improving the decay rates for the highest order (S-order) of spatial derivative of the solutions to the 3D system of compressible nematic liquid crystal. If the norms of both HS(S≥3)and for the initial value are bounded, as well as the norm of H3for that is small enough, with applying pure energy method, we give that the optimal decay rates for the highest order of spatial derivative of the solutions in norm of L2are (1+t)−(S2+α2), while that is just (1+t)−(S−12+α2)in Wei, Li and Yao’s study.展开更多
文摘本文的主要目的在于提高三维可压缩向列型液晶系统解的最高阶(S阶)空间导数的衰减率。如果初值的HS(S≥3)和范数都是有界的,并且其H3范数足够小,则应用纯能量法,我们给出了解的最高阶空间导数L2范数的最优衰减率为(1+t)−(S2+α2),而在魏,李和姚的研究中其衰减率仅为(1+t)−(S−12+α2)。Abstract: The major objective of this thesis lies in improving the decay rates for the highest order (S-order) of spatial derivative of the solutions to the 3D system of compressible nematic liquid crystal. If the norms of both HS(S≥3)and for the initial value are bounded, as well as the norm of H3for that is small enough, with applying pure energy method, we give that the optimal decay rates for the highest order of spatial derivative of the solutions in norm of L2are (1+t)−(S2+α2), while that is just (1+t)−(S−12+α2)in Wei, Li and Yao’s study.
