Global small solutions to heat conductive compressible nematic liquid crystal system: smallness on a scaling invariant quantity
Global small solutions to heat conductive compressible nematic liquid crystal system: smallness on a scaling invariant quantity
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DOI：
10.4310/cms.2023.v21.n6.a1
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发表时间：
2021-12
影响因子：
1
通讯作者：
Jinkai Li;Q. Tao
中科院分区：
文献类型：
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作者：
Jinkai Li;Q. Tao
本文研究了三维热传导可压缩液晶系统在真空和真空远场作用下的柯西问题。在尺度不变量$（\|\rho_0\|_\infty+1）\big[\|\rho_0\|_3+（\|\rho_0\|_\infty+1）^2（\|\sqrt{\rho_0}u_0\|_2^2+ \|\nabla d_0\|_2^2）\big] \big[\|\nabla u_0\|_2^2+（\|\rho_0\|_\infty+1）（\|\sqrt{\rho_0}E_0\|_2^2 + \|\nabla^2 d_0\|_2^2）\big]$是充分小的，其小性仅取决于系统中出现的参数。
In this paper, we consider the Cauchy problem to the three dimensional heat conducting compressible nematic liquid crystal system in the presence of vacuum and with vacuum far fields. Global well-posedness of strong solutions is established under the condition that the scaling invariant quantity $ (\|\rho_0\|_\infty+1)\big[\|\rho_0\|_3+(\|\rho_0\|_\infty+1)^2(\|\sqrt{\rho_0}u_0\|_2^2+ \|\nabla d_0\|_2^2)\big] \big[\|\nabla u_0\|_2^2+(\|\rho_0\|_\infty+1)(\|\sqrt{\rho_0}E_0\|_2^2 + \|\nabla^2 d_0\|_2^2)\big]$ is sufficiently small with the smallness depending only on the parameters appeared in the system.