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We consider global in time solutions of the Navier-Stokes-Fourier system describing the motion of a general compressible, viscous and heat conducting fluid far from equilibirum. Using a new concept of weak solution suitable to accommodate…

Analysis of PDEs · Mathematics 2021-09-03 Eduard Feireisl , Young-Sam Kwon

We consider an abstract functional-differential equation derived from the pressure-less Euler system with variable coefficients that includes several systems of partial differential equations arising in the fluid mechanics. Using the method…

Analysis of PDEs · Mathematics 2015-03-16 Eduard Feireisl

Our paper deals with three-dimensional nonsteady Navier-Stokes equations for non-Newtonian compressible fluids. It contains a~derivation of the relative energy inequality for the weak solutions to these equations. We show that the standard…

Analysis of PDEs · Mathematics 2022-10-25 Richard Andrášik , Václav Mácha , Rostislav Vodák

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…

Analysis of PDEs · Mathematics 2015-05-14 Marius Paicu , Arghir Zarnescu

Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…

Mathematical Physics · Physics 2018-10-10 Thomas Jankuhn , Maxim A. Olshanskii , Arnold Reusken

We consider the two-dimensional motion of the coupled system of a viscous incompressible fluid and a rigid disc moving with the fluid, in the whole plane. The fluid motion is described by the Navier-Stokes equations and the motion of the…

Analysis of PDEs · Mathematics 2015-05-27 Masoumeh Dashti , James C. Robinson

We prove weak-strong uniqueness results for the compressible Navier-Stokes system with degenerate viscosity coefficient and with vacuum in one dimension. In other words, we give conditions on the weak solution constructed in \cite{Jiu} so…

Analysis of PDEs · Mathematics 2014-12-01 Boris Haspot

We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong…

Analysis of PDEs · Mathematics 2015-05-13 Pierre Germain

In a previous paper [Jayanti, P.C., Trivisa, K. Local Existence of Solutions to a Navier-Stokes-Nonlinear-Schr\"odinger Model of Superfluidity. J. Math. Fluid Mech. 24, 46 (2022)], the authors proved the existence of local-in-time weak…

Analysis of PDEs · Mathematics 2022-04-01 Pranava Chaitanya Jayanti , Konstantina Trivisa

In the class of admissible weak solutions, we prove a weak-strong uniqueness result for the incompressible Euler equations assuming that the symmetric part of the gradient belongs to $L^1_{\rm loc}([0,+\infty);L^{\rm…

Analysis of PDEs · Mathematics 2023-09-07 Luigi De Rosa , Marco Inversi , Giorgio Stefani

The principle purpose of this work is to investigate a "viscous" version of a "simple" but still realistic bi-fluid model described in [Bresch, Desjardin, Ghidaglia, Grenier, Hillairet] whose "non-viscous" version is derived from physical…

Analysis of PDEs · Mathematics 2019-09-04 Antonin Novotny , Milan Pokorny

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, are presented. We show that these inconsistencies are consequences of…

Fluid Dynamics · Physics 2018-01-09 Magnus Svärd

We prove existence of time-periodic weak solutions to the coupled liquid-structure problem constituted by an incompressible Navier-Stokes fluid interacting with a rigid body of finite size, subject to an {\em undamped} linear restoring…

Analysis of PDEs · Mathematics 2023-09-14 Denis Bonheure , Giovanni P. Galdi

We study the motion of a compressible heat-conducting fluid in three dimensions interacting with a non-linear flexible shell. The fluid is described by the full Navier--Stokes--Fourier system. The shell constitutes an unknown part of the…

Analysis of PDEs · Mathematics 2021-11-18 Dominic Breit , Sebastian Schwarzacher

We consider the fluid-structure interaction problem of a viscous incompressible fluid contained in an elastic solid whose motion is not prescribed. The equations governing the motion of the solid are given by the Navier equations of linear…

Analysis of PDEs · Mathematics 2025-07-01 Giusy Mazzone

We investigate the evolution of rigid bodies in a viscous incompressible fluid. The flow is governed by the 2D Navier-Stokes equations, set in a bounded domain with Dirichlet boundary conditions. The boundaries of the solids and the domain…

Analysis of PDEs · Mathematics 2009-11-13 David Gérard-Varet , Matthieu Hillairet

We consider the Navier-Stokes system with Oseen and rotational terms describing the stationary flow of a viscous incompressible fluid around a rigid body moving at a constant velocity and rotating at a constant angular velocity. In a…

Analysis of PDEs · Mathematics 2015-11-13 Paul Deuring , Stanislav Kracmar , Sarka Necasova

We consider a single disk moving under the influence of a 2D viscous fluid and we study the asymptotic as the size of the solid tends to zero.If the density of the solid is independent of $\varepsilon$, the energy equality is not sufficient…

Analysis of PDEs · Mathematics 2016-11-08 Christophe Lacave , Takéo Takahashi

In this article, we consider Leray solutions of the Navier-Stokes equations in the exterior of one obstacle in 3D and we study the asymptotic behavior of these solutions when the obstacle shrinks to a curve or to a surface. In particular,…

Analysis of PDEs · Mathematics 2013-06-21 Christophe Lacave

We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densities and a soluble surfactant in a bounded domain of two or…

Analysis of PDEs · Mathematics 2026-01-13 Bohan Ouyang , Maurizio Grasselli , Hao Wu