具有大速度的三维非匀质不可压向列相液晶方程的全局适定性

Abstract

Abstract:

{In this paper, we investigate the the global well-posedness problem of the three-dimensional inhomogeneous incompressible nematic liquid crystal system with a class of large velocity. More precisely, assuming that the initial data $a_0\in\dot B_{p,1}^{\frac{3}{p}}, u_0\in\dot B_{p,1}^{\frac{3}{p}-1}, d_0\in\dot B_{p,1}^{\frac{3}{p}}$ satisfies

$C_{0}\left[\left\|u_{0}^{h}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}-1}}+\left(\left\|u_{0}^{3}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}-1}}+1\right)\left(\left\|a_{0}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}}}+\left\|d_{0}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}}}\right)\right] \exp \left\{C_{0}\left\|u_{0}^{3}\right\|_{\dot{B}_{p, 1}^{\frac{3}{p}-1}}^{2}\right\} \leq 1,$

then the nematic liquid crystal equation admits a unique global solution, where $C_0>0,~ 2\le p\le4.$

Key words: nematic liquid crystal system, large initial data, global well-posedness, vertical direction.

CLC Number:

O175.26

Dongxiang Chen, Qian He, Xiaoli Chen. Global Well-Posedness of the Three-Dimensional Inhomogeneous Incompressible Nematic Liquid Crystal System with a Class of Large Velocity[J].Acta mathematica scientia,Series A, 2026, 46(3): 996-1014.

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References 39

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Global Well-Posedness of the Three-Dimensional Inhomogeneous Incompressible Nematic Liquid Crystal System with a Class of Large Velocity

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