Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties

Wu, Hao; Xu, Xiang; Li, Chun

doi:10.1007/s00526-011-0460-5

Cited by 57 publications

(70 citation statements)

References 36 publications

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“…One of these models has been analyzed for example in [18] and [20] but only for periodic boundary conditions for (u, d). Therefore, the existence of weak solutions for these nematic models with stretching terms can be also deduced considering boundary conditions (1.9) or (1.10) for d. But, when time-dependent boundary data is considered for d, since these models have not a maximum principle for d, then we can only deduce the finite-time weak-regularity.…”

Section: Remark 112mentioning

confidence: 99%

Weak solutions for an initial–boundary Q-tensor problem related to liquid crystals

Guillén-González

Rodríguez-Bellido

2015

Nonlinear Analysis: Theory, Methods & Applications

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The coupled Navier-Stokes and Q-Tensor system is considered in a bounded three-dimensional domain under homogeneous Dirichlet boundary conditions for the velocity u and either nonhomogeneous Dirichlet or homogeneous Neumann boundary conditions for the tensor Q.The corresponding initial-value problem in the whole space R 3 was analyzed in [Paicu & Zarnescu, 2012].In this paper, three main results concerning weak solutions will be proved; the existence of global in time weak solutions (bounded up to infinite time), a uniqueness criteria and a maximum principle for Q. Moreover, we identify how to modify the system to deduce symmetry and traceless for Q, for any weak solution. The presence of a stretching term in the Q-system plays a crucial role in all the analysis.

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Section: Remark 112mentioning

confidence: 99%

Weak solutions for an initial–boundary Q-tensor problem related to liquid crystals

Guillén-González

Rodríguez-Bellido

2015

Nonlinear Analysis: Theory, Methods & Applications

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“…In this section, we intend to establish the higher regularity of the global weak solutions with sufficiently large viscosity of the fluid by using the energy argument shown in [20,25,26]. In order to finish the energy estimates, we need the following well-known lemma for Cauchy problem in dimension three.…”

Section: Global Existence Of Strong Solutionsmentioning

confidence: 99%

Global well-posedness for the dynamical Q-tensor model of liquid crystals

Huang

Ding

2015

Sci. China Math.

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In this paper, we consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.

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“…The existence of a unique global in time strong solution for a (u, p, d)-nematic model with stretching term and space-periodic boundary conditions for (u, d) is studied in [13] and [15].…”

Section: Remark 16mentioning

confidence: 99%

Weak Time Regularity and Uniqueness for a $Q$-Tensor Model

Guillén-González¹,

Rodríguez-Bellido²

2014

SIAM J. Math. Anal.

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The coupled Navier-Stokes and Q-Tensor system is one of the models used to describe the behavior of the nematic liquid crystals. The existence of weak solutions and a uniqueness criteria have been already studied (see [11] for a Cauchy problem in the whole R 3 and [7] for a initial-boundary problem in a bounded domain Ω).Nevertheless, results on strong regularity have only been treated in [11] for a Cauchy problem in the whole R 3 .In this paper, imposing Dirichlet or Neumann boundary conditions, we show the existence and uniqueness of a local in time weak solution with weak regularity for the time derivative of the velocity and the tensor variables (u, Q). Moreover, we gives a regularity criteria implying that this solution is global in time. Note that the regularity furnished by the weak regularity for (u, Q) and the weak regularity for (∂ t u, ∂ t Q) is not equivalent to the strong regularity.Finally, when large enough viscosity is imposed, we obtain the existence (and uniqueness) of global in time strong solution. In fact, if non-homogeneous Dirichlet condition for Q is imposed, the strong regularity needs to be obtained together with the weak regularity for (∂ t u, ∂ t Q).

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Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties

Cited by 57 publications

References 36 publications

Weak solutions for an initial–boundary Q-tensor problem related to liquid crystals

Weak solutions for an initial–boundary Q-tensor problem related to liquid crystals

Global well-posedness for the dynamical Q-tensor model of liquid crystals

Weak Time Regularity and Uniqueness for a $Q$-Tensor Model

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