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We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…

Analysis of PDEs · Mathematics 2025-08-20 Karoline Disser , Michelle Luckas

We present a general and systematic theory of non-equilibrium dynamics of multi-component fluid membranes, in general, and membranes containing transmembrane proteins, in particular. Developed based on a minimal number of principles of…

Soft Condensed Matter · Physics 2009-11-10 Michael A. Lomholt , Per L. Hansen , Ling Miao

This paper deals with the study of a three-dimensional model of thermomechanical coupling for viscous solids exhibiting hysteresis effects. This model is written in accordance with the formalism of generalized standard materials and it is…

Analysis of PDEs · Mathematics 2011-11-11 Laetitia Paoli , Adrien Petrov

We introduce a system of equations that models a non-isothermal magnetoviscoelastic fluid. We show that the model is thermodynamically consistent, and that the critical points of the entropy functional with prescribed energy correspond…

Analysis of PDEs · Mathematics 2023-05-24 Hengrong Du , Yuanzhen Shao , Gieri Simonett

We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…

Analysis of PDEs · Mathematics 2017-08-29 Amit Acharya , Gui-Qiang Chen , Siran Li , Marshall Slemrod , Dehua Wang

In this paper, we study a hyperbolic-parabolic coupled system arising in nonlinear three-dimensional thermoelasticity. We establish the global well-posedness and asymptotic behavior of solutions. Our main result shows that, a thermoelastic…

Analysis of PDEs · Mathematics 2026-03-11 Chuang Ma , Bin Guo

This paper presents a thermodynamically consistent model for multicomponent electrolyte solutions. The first part of this paper derives the general governing equations for nonequilibrium systems within the theory of nonequilibrium…

Analysis of PDEs · Mathematics 2016-05-25 Matthias Herz , Peter Knabner

Equations of motion are derived for (visco)elastic, self-gravitating, and variably-rotating planets. The equations are written using a decomposition of the elastic motion that separates the body's elastic deformation from its net…

Classical Physics · Physics 2023-09-25 Matthew Maitra , David Al-Attar

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the…

Statistical Mechanics · Physics 2015-03-19 Masafumi Fukuma , Yuho Sakatani

We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space. The motion of the fluid is modelled by the Navier-Stokes equations, whereas the motion of the rigid body is described by the…

Analysis of PDEs · Mathematics 2021-03-10 Jiao He , Dragos Iftimie

A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…

Soft Condensed Matter · Physics 2009-11-11 Thomas Ihle , Erkan Tuzel , Daniel M. Kroll

The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the surface Navier--Stokes equations with bending forces, the…

Fluid Dynamics · Physics 2023-06-21 Maxim A. Olshanskii

We propose a new approach to models of general compressible viscous fluids based on the concept of dissipative solutions. These are weak solutions satisfying the underlying equations modulo a defect measure. A dissipative solution coincides…

Analysis of PDEs · Mathematics 2020-01-01 Anna Abbatiello , Eduard Feireisl , Antonin Novotny

A linear system of differential equations describing a joint motion of thermoelastic porous body and thermofluid occupying porous space is considered. Although the problem is linear, it is very hard to tackle due to the fact that its main…

Analysis of PDEs · Mathematics 2007-05-23 Anvarbek M. Meirmanov

We consider the problem of motion of several rigid bodies immersed in a perfect compressible fluid. Using the method of convex integration we establish the existence of infinitely many weak solutions with {\it a priori} prescribed motion of…

Mathematical Physics · Physics 2019-10-23 Eduard Feireisl , Václav Mácha

Thermal gradients lead to macroscopic fluid motion if a confining surface is present along the gradient. This fundamental nonequilibrium effect, known as thermo-osmosis, is held responsible for particle thermophoresis in colloidal…

Statistical Mechanics · Physics 2019-07-17 Pietro Anzini , Gaia Maria Colombo , Zeno Filiberti , Alberto Parola

We consider a model for an incompressible visoelastic fluid. It consists of the Navier-Stokes equations involving an elastic term in the stress tensor and a transport equation for the evolution of the deformation gradient. The novel feature…

Analysis of PDEs · Mathematics 2019-10-23 Martin Kalousek

A thermodynamically consistent visco-elastodynamical model at finite strains is derived that also allows for inelasticity (like plasticity or creep), thermal coupling, and poroelasticity with diffusion. The theory is developed in the…

Mathematical Physics · Physics 2024-04-17 Alexander Mielke , Tomáš Roubíček

Viscoelastic rate-type fluid models are essential for describing the behavior of a wide range of complex materials, with applications in fields such as engineering, biomaterials, and medicine. These models are particularly useful for…

Analysis of PDEs · Mathematics 2025-05-01 Miroslav Bulìček , Jakub Woźnicki

Historically, the thermodynamic behavior of gasses was described first and the derived equations were adapted to solids. It is suggested that the current thermodynamic description of solid phase is still incomplete because the isothermal…

Chemical Physics · Physics 2010-02-24 Jozsef Garai