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The existence of weak solutions to the obstacle problem for a nonlocal semilinear fourth-order parabolic equation is shown, using its underlying gradient flow structure. The model governs the dynamics of a microelectromechanical system with…

Analysis of PDEs · Mathematics 2019-10-10 Philippe Laurençot , Christoph Walker

In three space dimensions, we consider the compressible inviscid model describing the time evolution of two fluids sharing the same velocity and enjoying the algebraic pressure closure. By employing the technique of convex integration, we…

Analysis of PDEs · Mathematics 2019-12-24 Yang Li , Ewelina Zatorska

We consider a diffuse interface model for an incompressible isothermal mixture of two viscous Newtonian fluids with different densities in a bounded domain in two or three space dimensions. The model is the nonlocal version of the one…

Analysis of PDEs · Mathematics 2015-06-01 Sergio Frigeri

We study a system of equations governing liquid and gas flow in porous media. The gas phase is homogeneous while the liquid phase is composed of a liquid component and dissolved gas component. It is assumed that the gas component is weakly…

Analysis of PDEs · Mathematics 2018-04-23 Mladen Jurak , Ivana Radisic , Ana Zgaljic Keko

We consider a real two-fluid system of compressible viscous fluids with a common velocity field and algebraic closure for the pressure law. The constitutive relation involves densities of both fluids through an implicit function. The…

Analysis of PDEs · Mathematics 2026-02-24 Yang Li , Mária Lukáčová-Medvid'ová , Milan Pokorný , Ewelina Zatorska

We consider the Cauchy problem for incompressible viscoelastic fluids in the whole space $\mathbb{R}^d$ ($d=2,3$). By introducing a new decomposition via Helmholtz's projections, we first provide an alternative proof on the existence of…

Analysis of PDEs · Mathematics 2023-07-28 Xianpeng Hu , Hao Wu

We study a stationary 3D/2D fluid-structure interaction problem between an elastic structure described by the linear plate equation and a fluid described by the compressible Navier-Stokes equations with hard-sphere pressure and…

Analysis of PDEs · Mathematics 2026-03-30 Boris Muha , Šárka Nečasová , Milan Pokorný , Srđan Trifunović , Justin T. Webster

We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids with different densities in a bounded domain in two and three space dimensions. In contrast to previous works, we…

Analysis of PDEs · Mathematics 2019-11-21 Helmut Abels , Yutaka Terasawa

We consider a phase field model for the flow of two partly miscible incompressible, viscous fluids of Non-Newtonian (power law) type. In the model it is assumed that the densities of the fluids are equal. We prove existence of weak…

Analysis of PDEs · Mathematics 2013-02-14 Helmut Abels , Lars Diening , Yutaka Terasawa

We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of…

Analysis of PDEs · Mathematics 2025-08-26 Piotr B. Mucha , Sarka Necasova , Maja Szlenk

In this article, we study a non-Newtonian Stokes-Transport system. This set of PDEs was introduced as a model for describing the behavior of a cloud of particles in suspension in a Stokes fluid, and is a nonlinear coupling between a…

Analysis of PDEs · Mathematics 2024-01-08 Dimitri Cobb , Geoffrey Lacour

We consider a circulation system arising in turbulence modelling in fluid dynamics with unbounded eddy viscosities. Various notions of weak solutions are considered and compared. We establish existence and regularity results. In particular…

Analysis of PDEs · Mathematics 2007-10-03 Pierre Dreyfuss

We study a nonlinear fluid-structure interaction problem in which the fluid is described by the three-dimensional incompressible Navier-Stokes equations, and the elastic structure is modeled by the nonlinear plate equation which includes a…

Analysis of PDEs · Mathematics 2019-06-05 Srđan Trifunović , Ya-Guang Wang

The flow of two macroscopically immiscible, viscous, incompressible fluids with unmatched densities is studied, where a transfer of mass between the constituents by phase transition is taken into account. To this end, two…

Analysis of PDEs · Mathematics 2025-05-09 Helmut Abels , Harald Garcke , Julia Wittmann

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

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

We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…

Analysis of PDEs · Mathematics 2014-06-09 Michela Eleuteri , Elisabetta Rocca , Giulio Schimperna

We consider the compressible Navier-Stokes system with variable entropy. The pressure is a nonlinear function of the density and the entropy/potential temperature which, unlike in the Navier-Stokes-Fourier system, satisfies only the…

Analysis of PDEs · Mathematics 2016-03-31 David Maltese , Martin Michalek , Piotr B. Mucha , Antonin Novotny , Milan Pokorny , Ewelina Zatorska

Of concern is the study of a system of three equations describing the motion of a viscous complete wetting two-phase thin film endowed with a layer of insoluble surfactant on the surface of the upper fluid under the effects of capillary…

Analysis of PDEs · Mathematics 2016-08-30 Gabriele Bruell

We study a doubly nonlinear parabolic problem arising in the modeling of gas transport in pipelines. Using convexity arguments and relative entropy estimates we show uniform bounds and exponential stability of discrete approximations…

Analysis of PDEs · Mathematics 2023-05-31 Herbert Egger , Jan Giesselmann