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1.
In this paper, we establish a blowup criterion for the two-dimensional compressible nematic liquid crystal flows. The criterion is given in terms of the density and the gradient of direction field, where the later satisfies the Serrin-type blowup criterion. For this result, we do not need the initial density to be positive.  相似文献
2.
In this paper, we are concerned with the regularity of solutions to the liquid crystal flows with rough initial data in RnRn. We prove that the solution constructed by Wang (2011) in [23] has higher regularity. Moreover we obtain a decay estimate in time for any space derivative.  相似文献
3.
首先, 本文利用标准的能量估计方法得到高维(3 维及以上) 的液晶流方程组小初值经典解的整体存在性. 然后, 本文运用Green 函数方法, 得到奇数维情形(3 维及以上) 该解的逐点估计. 该结果表明, 密度ρ和动量m同Navier-Stokes 方程组一样满足一般Huygens 原理, 而单位向量场d则没有这种现象, 其有着与热方程的解类似的时空估计.  相似文献
4.
In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in three-dimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial datas are close to the constant equilibrium state in H2-framework. If the initial datas in L1-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.  相似文献
5.
This paper is concerned with the short time strong solutions for Cauchy problem to a simplified Ericksen–Leslie system of compressible nematic liquid crystals in two dimensions with vacuum as far field density. We establish a blow‐up criterion for possible breakdown of such solutions at a finite time, which is analogous to the well‐known Serrin's blow‐up criterion for the incompressible Navier–Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献
6.
In this paper, we provide a sufficient condition, in terms of the horizontal gradient of two horizontal velocity components and the gradient of liquid crystal molecular orientation field, for the breakdown of local in time strong solutions to the three‐dimensional incompressible nematic liquid crystal flows. More precisely, let T be the maximal existence time of the local strong solution (u ,d ), then T <+ if and only if where u h =(u 1,u 2), ∇h =(1,2). This result can be regarded as the generalization of the well‐known Beale‐Kato‐Majda (BKM) type criterion and is even new for the three‐dimensional incompressible Navier–Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献
7.
The paper is concerned with a simplified system, proposed by Ericksen [6] and Leslie [20], modeling the flow of nematic liquid crystals. In the first part, we give a new Serrin's continuation principle for strong solutions of general compressible liquid crystal flows. Based on new observations, we establish a localized Serrin's regularity criterion for the 3D compressible spherically symmetric flows. It is proved that the classical solution loses its regularity in finite time if and only if, either the concentration or vanishing of mass forms or the norm inflammation of gradient of orientation field occurs around the center.  相似文献
8.
9.
We consider the temporal decay estimates for weak solutions to the two‐dimensional nematic liquid crystal flows, and we show that the energy norm of a global weak solution has non‐uniform decay under suitable conditions on the initial data. We also show the exact rate of the decay (uniform decay) of the energy norm of the global weak solution.  相似文献
10.
In this article, first of all, the global existence and asymptotic stability of solutions to the incompressible nematic liquid crystal flow is investigated when initial data are a small perturbation near the constant steady state (0,δ0); here, δ0 is a constant vector with |δ0|=1. Precisely, we show the existence and asymptotic stability with small initial data for . The initial data class of us is not entirely included in the space BMO−1×BMO and contains strongly singular functions and measures. As an application, we obtain a class of asymptotic existence of a basin of attraction for each self‐similar solution with homogeneous initial data. We also study global existence of a large class of decaying solutions and construct an explicit asymptotic formula for ∣x∣→, relating the self‐similar profile (U(x),D(x)) to its corresponding initial data (u0,d0). In two dimensions, we obtain higher‐order asymptotics of (u(x),d(x)). Copyright © 2016 John Wiley & Sons, Ltd.  相似文献
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