|
|
 |
| |
|
|
|
On the blow up criterion for the 3D nematic liquid crystal flows involving the second eigenvalue of the deformation tensor |
|
|
|
PP: 539-545 |
|
|
|
doi:10.18576/amis/170401
|
|
|
|
Author(s) |
|
|
|
Ines Ben Omrane,
|
|
|
|
Abstract |
|
|
| In this paper, we study the blow up criterion of the smooth solutions to the three-dimensional incompressible nematic liquid crystal flows in terms of $\lambda _{2}^{+}$ in the multiplier space $\dot{X}_{1}$ and $\nabla d$ in $BMO$. It is shown that the solution $(u,d)$ can be extended beyond $t=T$ if
T λ + ( · , t ) 2 2
2 X ̇ 1 + ∥ ∇ d ( · , t ) ∥ B M O d t < ∞ .
0 ln(e+∥∇u(·,t)∥X ̇1) ln(e+∥∇d(·,t)∥BMO) |
|
|
|
|
|
|
|
