English
Related papers

Related papers: Weak compactness of simplified nematic liquid flow…

200 papers

We study uniaxial energy minimizers within the Landau-de Gennes theory for nematic liquid crystals, subject to dirichlet boundary conditions. Topological defects in such minimizers correspond to the zeros of the corresponding equilibrium…

Analysis of PDEs · Mathematics 2010-05-31 Apala Majumdar

In this paper, we are concerned with the initial-Neumann boundary value problem of the Schr\"{o}dinger flow for maps from a smooth bounded domain in an Euclidean space into $\mathbb{S}^2$. By adopting a novel method due to B. Chen and Y.D.…

Analysis of PDEs · Mathematics 2026-04-10 Bo Chen , Guangwu Wang , Youde Wang

We analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modelled by…

Analysis of PDEs · Mathematics 2023-02-13 Martin Kalousek , Sourav Mitra , Šárka Nečasová

We introduce a simple model of the time evolution of a binary mixture of compressible fluids including the thermal effects. Despite its apparent simplicity, the model is thermodynamically consistent admitting an entropy balance equation. We…

Analysis of PDEs · Mathematics 2021-09-07 Eduard Feireisl , Madalina Petcu , Bangwei She

We study the asymptotic behaviour, as a small parameter $\varepsilon$ tends to zero, of minimisers of a Ginzburg-Landau type energy with a nonlinear penalisation potential vanishing on a compact submanifold $\mathcal{N}$ and with a given…

Analysis of PDEs · Mathematics 2022-08-18 Antonin Monteil , Rémy Rodiac , Jean Van Schaftingen

We consider the compressible Navier-Stokes system describing the motion of a viscous fluid confined to a straight layer $\Omega_{\delta}=(0,\delta)\times\mathbb{R}^2$. We show that the weak solutions in the 3D domain converge strongly to…

Analysis of PDEs · Mathematics 2020-01-29 Matteo Caggio , Donatella Donatelli , Sarka Necasova , Yongzhong Sun

The present contribution investigates the well-posedness of a PDE system describing the evolution of a nematic liquid crystal flow under kinematic transports for molecules of different shapes. More in particular, the evolution of the {\em…

Analysis of PDEs · Mathematics 2015-05-28 Cecilia Cavaterra , Elisabetta Rocca

We prove existence of global weak solutions to the chemotaxis system $ u_t=\Delta u - \nabla\cdot (u\nabla v) +\kappa u -\mu u^2 $ $ v_t=\Delta v-v+u $ under homogeneous Neumann boundary conditions in a smooth bounded convex domain…

Analysis of PDEs · Mathematics 2014-07-21 Johannes Lankeit

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…

Analysis of PDEs · Mathematics 2023-07-19 Jinrui Huang , Shijin Ding

The paper analyses a possible occurrence of soft and semi-soft dissipative modes in uniaxially anisotropic nematic liquids as described by the five parametric Leslie-Ericksen-Parodi (LEP) constitutive equations (CEs). As in the similar…

Soft Condensed Matter · Physics 2007-05-23 Arkady I. Leonov , Valery S. Volkov

A compactness framework is formulated for the incompressible limit of approximate solutions with weak uniform bounds with respect to the adiabatic exponent for the steady Euler equations for compressible fluids in any dimension. One of our…

Analysis of PDEs · Mathematics 2016-06-22 Gui-Qiang G. Chen , Feimin Huang , Tian-Yi Wang , Wei Xiang

This article investigates the interaction of nematic liquid crystals modeled by a simplified Ericksen-Leslie model with a rigid body. It is shown that this problem is locally strongly well-posed, and that it also admits a unique, global…

Analysis of PDEs · Mathematics 2024-09-04 Tim Binz , Felix Brandt , Matthias Hieber , Arnab Roy

We prove the existence of global weak entropy solutions for a class of non-symmetric Keyfitz-Kranzer type systems that includes lubrication models for thin-film flow. We identify a family of entropy/entropy-flux pairs for these first-order…

Analysis of PDEs · Mathematics 2026-04-20 Rahul Barthwal , Philipp Öffner , Christian Rohde

We study the static equilibria of a simplified Leslie--Ericksen model for a unidirectional uniaxial nematic flow in a prototype microfluidic channel, as a function of the pressure gradient $\mathcal{G}$ and inverse anchoring strength,…

Analysis of PDEs · Mathematics 2017-06-28 Maria Crespo , Ian Griffiths , Apala Majumdar , Angel Ramos

We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a…

Analysis of PDEs · Mathematics 2017-01-03 Helmut Abels , Dominic Breit

In this note, we prove the existence of weak solutions of the Chern-Ricci flow through blow downs of exceptional curves, as well as backwards smooth convergence away from the exceptional curves on compact complex surfaces. The smoothing…

Differential Geometry · Mathematics 2017-01-19 Xiaolan Nie

In this paper, we prove the existence and uniqueness of local strong solutions of the hydrodynamics of nematic liquid crystals system under the initial data satisfying a natural compatibility condition. Also the global strong solutions of…

Functional Analysis · Mathematics 2011-07-01 Xiangao Liu , Lanming Liu , Yihang Hao

In this article we examine the interaction of incompressible 2D flows with compact material boundaries. Our focus is the dynamic behavior of the circulation of velocity around boundary components and the possible exchange between flow…

Analysis of PDEs · Mathematics 2013-05-07 Dragos Iftimie , Milton Lopes Filho , Helena Nussenzveig Lopes , Franck Sueur

In this paper, we consider unsaturated poroelasticity, i.e., coupled hydro-mechanical processes in unsaturated porous media, modeled by a non-linear extension of Biot's quasi-static consolidation model. The coupled, elliptic-parabolic…

Analysis of PDEs · Mathematics 2019-09-17 Jakub Wiktor Both , Iuliu Sorin Pop , Ivan Yotov

The work deals with the Ericksen-Leslie model for nematic liquid crystals on the whole space, the half-space and on exterior domains with smooth boundary. The crystal orientation is described by a unit vector that is a small perturbation of…

Analysis of PDEs · Mathematics 2024-09-19 Daniele Barbera , Vladimir Georgiev