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We consider the Quantum Navier-Stokes system in three space dimensions. We prove compactness of finite energy weak solutions for large initial data. The main novelties are that vacuum regions are included in the weak formulation and no…

Analysis of PDEs · Mathematics 2016-05-13 Paolo Antonelli , Stefano Spirito

In [1], the Authors rigorously establish the relaxation limit from the Quantum Navier Stokes Poisson (QNSP) system to the Quantum Drift Diffusion (QDD) equation, while providing only a brief outline of the global existence theory for weak…

Analysis of PDEs · Mathematics 2025-12-10 Giada Cianfarani Carnevale

In this paper we consider the Quantum Navier-Stokes system both in two and in three space dimensions and prove global existence of finite energy weak solutions for large initial data. In particular, the notion of weak solutions is the…

Analysis of PDEs · Mathematics 2021-03-30 Paolo Antonelli , Stefano Spirito

We study the lagrangian structure for weak solutions of two dimensional Navier-Stokes equations for a non-barotropic compressible fluid, i.e. we show the uniqueness of particle trajectories for two dimensional compressible fluids including…

Analysis of PDEs · Mathematics 2018-10-29 Pedro Maluendas , Marcelo M. Santos

We consider the compressible (barotropic) Navier-Stokes system on time-dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behaviour, viscosity, and the pressure in the weak…

Analysis of PDEs · Mathematics 2015-04-01 Eduard Feireisl , Ondřej Kreml , Šárka Nečasová , Jiří Neustupa , Jan Stebel

A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard…

Analysis of PDEs · Mathematics 2013-01-14 Sergio Frigeri , Maurizio Grasselli , Pavel Krejčí

In the spirit of D. Hoff's weak solution theory for the compressible Navier-Stokes equations (CNS) with bounded density, in this paper we establish the global existence and regularity properties of finite-energy weak solutions to an initial…

Analysis of PDEs · Mathematics 2025-09-03 Jin Tan , Yan-Lin Wang , Lan Zhang

This paper concerns the existence of global weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients. We construct suitable approximate system which has smooth solutions satisfying the…

Analysis of PDEs · Mathematics 2015-11-12 Jing Li , Zhouping Xin

In this paper we prove the existence of global weak dissipative martingale solutions for a one-dimensional compressible fluid model with capillarity and density dependent viscosity, driven by random initial data and a stochastic forcing…

Analysis of PDEs · Mathematics 2024-12-17 Donatella Donatelli , Lorenzo Pescatore , Stefano Spirito

We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that…

Analysis of PDEs · Mathematics 2014-04-08 Peter Bella , Eduard Feireisl , Bum Ja Jin , Antonin Novotny

We propose and analyze a finite element method for a semi-stationary Stokes system modeling compressible fluid flow subject to a Navier-slip boundary condition. The velocity (momentum) equation is approximated by a mixed finite element…

Numerical Analysis · Mathematics 2009-04-07 Kenneth H. Karlsen , Trygve K. Karper

We prove strong convergence of an upwind-type finite volume method to a weak solution of the Navier-Stokes-Fourier system with the Dirichlet boundary conditions. The limit solution satisfies a weak form of the mass and momentum equations,…

Numerical Analysis · Mathematics 2026-03-24 Eduard Feireisl , Maria Lukacova-Medvidova , Bangwei She , Yuhuan Yuan

We consider the Navier--Stokes--Fourier system in a bounded domain $\Omega \subset R^d$, $d=2,3$, with physically realistic in/out flow boundary conditions. We develop a new concept of weak solutions satisfying a general form of relative…

Analysis of PDEs · Mathematics 2021-05-12 Eduard Feireisl , Antonin Novotny

We show the weak-strong uniqueness property for the compressible Navier-Stokes system with general non-monotone pressure law. A weak solution coincides with the strong solution emanating from the same initial data as long as the latter…

Analysis of PDEs · Mathematics 2018-06-26 Eduard Feireisl

A well-known diffuse interface model consists of the Navier-Stokes equations nonlinearly coupled with a convective Cahn-Hilliard type equation. This system describes the evolution of an incompressible isothermal mixture of binary-fluids and…

Analysis of PDEs · Mathematics 2011-02-22 Pierluigi Colli , Sergio Frigeri , Maurizio Grasselli

We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type. The plate is situated at the top of…

Analysis of PDEs · Mathematics 2020-10-05 Sebastian Schwarzacher , Matthias Sroczinski

In this manuscript, we aim to establish global existence of weak solutions with higher regularity to the compressible Navier-Stokes equations under no-slip boundary conditions. Though Lions\cite{L1} and Feireisl\cite{F1} have established…

Analysis of PDEs · Mathematics 2024-11-05 Xiangdi Huang , Zhouping Xin , Wei Yan

We study a diffuse-interface model that describes the dynamics of two-phase incompressible flows driven by the thermo-induced Marangoni effect. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity, the…

Analysis of PDEs · Mathematics 2026-05-26 Lingxi Chen , Hao Wu

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations with damping is proved for large data in three dimensional space. The model consists of the compressible Navier-Stokes equations…

Analysis of PDEs · Mathematics 2015-08-26 Alexis F. Vasseur , Cheng Yu

In this paper, a dissipative version of a compressible one velocity Baer--Nunziato type system for a mixture of two compressible heat conducting gases is considered. The complete existence proof for weak solutions to this system was…

Analysis of PDEs · Mathematics 2025-09-24 Martin Kalousek , Šárka Nečasová