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Article overview
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Global strong solution to the two-dimensional density-dependent nematic liquid crystal flows with vacuum | Lin Li
; Qiao Liu
; Xin Zhong
; | Date: |
2 Aug 2015 | Abstract: | We are concerned with the Cauchy problem of the two-dimensional (2D)
nonhomogeneous incompressible nematic liquid crystal flows on the whole space
$mathbb{R}^{2}$ with vacuum as far field density. It is proved that the 2D
nonhomogeneous incompressible nematic liquid crystal flows admits a unique
global strong solution provided the initial data density and the gradient of
orientation decay not too slow at infinity, and the basic energy
$|sqrt{
ho_0}mathbf{u}_0|_{L^2}^2+|
ablamathbf{d}_0|_{L^2}^2$ is
small. In particular, the initial density may contain vacuum states and even
have compact support. Moreover, the large time behavior of the solution is also
obtained. | Source: | arXiv, 1508.0235 | Services: | Forum | Review | PDF | Favorites |
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