9 papers · 1 filter
Variational principles for the interaction of liquid crystals and electric fields in the Oseen--Frank model
Giovanni Di Fratta, Valeriy Slastikov, Arghir Zarnescu
We develop a rigorous variational framework for uniaxial nematic liquid crystals interacting with an external electric field in the one-constant Oseen--Frank approximation. Equilib…
On the impact of clusters of rigid balls on the motion of a viscous fluid
Marco Bravin, Eduard Feireisl, Arnab Roy +1
We develop a new approach to the problem of the motion of a large number of rigid bodies immersed in a viscous fluid. The leading idea is the concept of cluster - a collection of i…
The Ginzburg-Landau system with general potential: maximum principle and gradient estimates
Radu Ignat, Luc Nguyen, Valeriy Slastikov +1
We study critical points of the Ginzburg-Landau energy functional $$\mathcal{F}_\varepsilon[u] = \int_Ω\Big[ \frac{1}{2}|\nabla u|^2 + \frac{1}{2\varepsilon^2} W(1 - |u|^2)\Big]\,…
On the long time behaviour of a system of several rigid bodies immersed in a viscous fluid
Marco Bravin, Eduard Feireisl, Arnab Roy +1
We consider several rigid bodies immersed in a viscous Newtonian fluid contained in a bounded domain in . We introduce a new concept of dissipative weak solution of the proble…
A not-so-strange term coming from somewhere
Giacomo Canevari, Kirill Cherednichenko, Arghir Zarnescu
We consider Laplace's equation in a periodically perforated domain with Robin boundary conditions on the holes, where the Robin coefficient is scaled proportionally to the inverse…
Variational Dual Solutions for Incompressible Fluids
Amit Acharya, Bianca Stroffolini, Arghir Zarnescu
We consider a construction proposed in \cite{acharyaQAM} that builds on the notion of weak solutions for incompressible fluids to provide a scheme that generates variationally a ce…