Related papers: Strict Physicality of Global Weak Solutions of a N…
In this paper, we study a coupled compressible Navier-Stokes/Q-tensor system modeling the nematic liquid crystal flow in a three-dimensional bounded spatial domain. The existence and long time dynamics of globally defined weak solutions for…
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 strong solutions that are uniformly…
This paper is devoted to the full system of incompressible liquid crystals, as modeled in the Q-tensor framework. The main purpose is to establish the uniqueness of weak solutions in a two dimensional setting, without imposing an extra…
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…
In this paper we prove the existence of global in time weak solutions for an evolutionary PDE system modelling nonisothermal Landau-de Gennes nematic liquid crystal (LC) flows in three dimensions of space. In our model, the incompressible…
We study a complex non-newtonian fluid that models the flow of nematic liquid crystals. The fluid is described by a system that couples a forced Navier-Stokes system with a parabolic-type system. We prove the existence of global weak…
We study the global existence and regularity of solutions for a system describing the evolution of a nematic liquid crystal fluid. The fluid is described by a system that couples a forced Navier-Stokes system with a parabolic-type system.…
In this paper, we establish the global existence of a suitable weak solution to the co-rotational Beris-Edwards $Q$-tensor system modeling the hydrodynamic motion of nematic liquid crystals with either Landau-De Gennes bulk potential in…
We consider a dissipative quantum fluid on the whole space $\mathbb{R}^d$ ($d\geq 1$) confined by an external harmonic potential. The dynamics of the quantum fluid is described by the Quantum Navier-Stokes (QNS) system which is a particular…
We study a Q-tensor problem modeling the dynamic of nematic liquid crystals in 3D domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the elastic forces of the liquid crystal, coupled with…
We study the three-dimensional compressible Navier-Stokes equations coupled with the $Q$-tensor equation perturbed by a multiplicative stochastic force, which describes the motion of nematic liquid crystal flows. The local existence and…
We prove global existence of weak solutions to two systems of equations which extend the dynamics of the Navier-Stokes equations for incompressible viscous flow with no-slip boundary condition. The systems of equations we consider arise as…
We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows with chemotaxis effect. The PDE system couples a Navier-Stokes equation for the fluid velocity, a convective Cahn-Hilliard equation for the…
A complex non-Newtonian fluid models the nematic liquid crystal flows confined in a bounded domain in $\mathbb{R}^3$ is considered. The system is a forced incompressible Navier-Stokes equation coupled with a parabolic type Q-tensor flows.…
In this paper, we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the Beris-Edwards model of nematic liquid crystals in $\R^3$ with an arbitrary parameter $\xi\in\R$, which measures the ratio of tumbling and…
We consider here an elliptic coupled system describing the dynamics of liquid crystals flows. This system is posed on the whole n-dimensional space. We introduce first the notion of very weak solutions for this system. Then, within the…
A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard…
In [1], the Authors rigorously establish the relaxation limit from the Quantum Navier Stokes Poisson (QNSP) system to the Quantum Drift Diffusion (QDD) equation, while providing only a brief outline of the global existence theory for weak…
We show the existence of global-in-time weak solutions to a general class of coupled bead-spring chain models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids with noninteracting polymer chains,…
In this paper, we study the global well-posedness of a coupled system of kinetic and fluid equations. More precisely, we establish the global existence of weak solutions for Navier-Stokes-BGK system consisting of the BGK model of Boltzmann…