# Regularity Problem for the Nematic LCD System with Q-tensor in ℝ3

@article{Dai2016RegularityPF, title={Regularity Problem for the Nematic LCD System with Q-tensor in ℝ3}, author={Mimi Dai}, journal={SIAM J. Math. Anal.}, year={2016}, volume={49}, pages={5007-5030} }

We study the regularity problem of a nematic liquid crystal model with local configuration represented by Q-tensor in three dimensions. It was an open question whether the classical Prodi-Serrin condition implies regularity for this model. Applying a wavenumber splitting method, we show that a solution does not blow-up under certain extended Beale-Kato-Majda condition solely imposed on velocity. This regularity criterion automatically implies that the classical Prodi-Serrin or Beale-Kato-Majda…

## 3 Citations

### Global well-posedness of the two dimensional Beris–Edwards system with general Laudau–de Gennes free energy

- MathematicsJournal of Differential Equations
- 2019

### Low modes regularity criterion for a chemotaxis-Navier-Stokes system

- MathematicsCommunications on Pure & Applied Analysis
- 2020

In this paper we study the regularity problem of a three dimensional chemotaxis-Navier-Stokes system on a periodic domain. A new regularity criterion in terms of only low modes of the oxygen…

### Applications of harmonic analysis techniques to regularity problems of dissipative equations

- MathematicsContemporary Mathematics
- 2020

We discuss recent advances in the regularity problem of a variety of fluid equations and systems. The purpose is to illustrate the advantage of harmonic analysis techniques in obtaining sharper…

## References

SHOWING 1-10 OF 26 REFERENCES

### Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions

- MathematicsAdvances in Differential Equations
- 2016

Existence and uniqueness of local strong solution for the Beris--Edwards model for nematic liquid crystals, which couples the Navier-Stokes equations with an evolution equation for the Q-tensor, is…

### Strict Physicality of Global Weak Solutions of a Navier-Stokes Q-tensor System with Singular Potential

- Mathematics
- 2012

We study the existence, regularity and so-called `strict physicality' of weak solutions of a coupled Navier-Stokes Q-tensor system which is proposed as a model for the incompressible flow of nematic…

### Energy Dissipation and Regularity for a Coupled Navier–Stokes and Q-Tensor System

- Mathematics
- 2012

We study a complex non-Newtonian fluid that models the flowof nematic liquid crystals. The fluid is described by a system that couples a forced Navier–Stokes system with a parabolic-type system. We…

### Long-time Behavior for Nonlinear Hydrodynamic System Modeling the Nematic Liquid Crystal Flows

- Mathematics
- 2009

We study a simplified system of the original Ericksen--Leslie equations for the flow of nematic liquid crystals. This is a coupled non-parabolic dissipative dynamic system. We show the convergence of…

### Global strong solutions of the full Navier-Stokes and $Q$-tensor system for nematic liquid crystal flows in $2D$: existence and long-time behavior

- Mathematics
- 2015

We consider a full Navier-Stokes and $Q$-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global…

### Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory

- Physics
- 2010

We define a continuum energy functional that effectively interpolates between the mean-field Maier-Saupe energy and the continuum Landau-de Gennes energy functional and can describe both spatially…

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

- MathematicsSIAM J. Math. Anal.
- 2014

The coupled Navier--Stokes and $Q$-tensor system is one of the models used to describe the behavior of nematic liquid crystals. The existence of weak solutions and a uniqueness criterion have been…

### On asymptotic isotropy for a hydrodynamic model of liquid crystals

- MathematicsAsymptot. Anal.
- 2016

Using the method of Fourier splitting, it is shown that solutions of the system tend to the isotropic state at the rate (1+ t)−β as t→∞ for a certain β > 1 2 .

### Global Existence and Regularity for the Full Coupled Navier-Stokes and Q-Tensor System

- MathematicsSIAM J. Math. Anal.
- 2011

Under certain conditions it is proved the global existence of weak solutions in dimension two or three and the existence of global regular solutions in Dimension two and the weak-strong uniqueness of the solutions, for sufficiently regular initial data.