Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898854 | Journal of Differential Equations | 2018 | 33 Pages |
Abstract
In this paper, we investigate the global existence and uniqueness of solution to the 3D inhomogeneous incompressible nematic liquid crystal flows with variable density in the framework of Besov spaces. It is proved that there exists a global and unique solution to the nematic liquid crystal flows if the initial data (Ï0â1,u0,n0âe3)âM(BËp,13pâ1(R3))ÃBËp,13pâ1(R3)ÃBËp,13p(R3) with 1â¤p<6, and satisfiesâÏ0â1âM(BËp,13pâ1)+âu0âBËp,13pâ1+ân0âe3âBËp,13pâ¤cfor some small c>0 depending only on p. Here M(BËp,13pâ1(R3)) is the multiplier space of Besov space BËp,13p(R3). Using the Lagrangian approach in Danchin and Mucha (2012, 2013) [7], [8] is the key to our results.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xianpeng Hu, Qiao Liu,