Name
Title | ||
|---|---|---|
On Well-Posedness and Decay of Strong Solutions for 3D Incompressible Smectic-A Liquid Crystal Flows |
Abstract | ||
|---|---|---|
In this paper, we study a hydrodynamic system that models smectic-A liquid crystal flow in
$${\mathbb {R}}^3$$
. This model consists of the Navier–Stokes equations for fluid velocity coupled with a fourth-order equation for the layer variable. The main purpose is to analyze the well-posedness and asymptotic behavior of strong solutions. We first prove the local well-posedness through the higher-order a prior estimates of the solution and Galerkin method. Then, we establish the existence of global strong solution provided that
$$ \Vert u_0 \Vert _{ \dot{H }^{\frac{1}{2} }} +\Vert \varphi _0\Vert _{\dot{ H} ^{\frac{3}{2} }} +\Vert \varphi _0\Vert _{\dot{ H} ^{\frac{7}{2} }} $$
is sufficiently small. Finally, we show the temporary decay estimates for the higher-order derivatives of strong solution by using the negative Sobolev norm estimates. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1007/s00332-021-09771-9 | Journal of Nonlinear Science |
Keywords | DocType | Volume |
Smectic-A liquid crystal flows, Strong solutions, Local well-posedness, Global well-posedness, Decay estimates, 35D35, 35Q35, 76A15 | Journal | 32 |
Issue | ISSN | Citations |
1 | 0938-8974 | 0 |
PageRank | References | Authors |
0.34 | 1 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhao, Xiaopeng | 1 | 0 | 0.34 |
| Yong Zhou | 2 | 1 | 2.17 |