English
Related papers

Related papers: Finite-energy solutions for compressible two-fluid…

200 papers

This work is devoted to the global existence of weak solution for a general isothermal model of capillary fluids derived by C. Rohde, which can be used as a phase transition model. This article is structured in the following way: first of…

Analysis of PDEs · Mathematics 2008-03-14 Boris Haspot

In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove global existence of finite energy weak solutions for large initial data. Contrary…

Analysis of PDEs · Mathematics 2019-03-07 Paolo Antonelli , Stefano Spirito

The paper aims on the construction of weak solutions to equations of a model of compressible viscous fluids, being a simplification of the classical compressible Navier-Stokes system. We present a novel scheme for approximating systems that…

Analysis of PDEs · Mathematics 2024-09-26 Nilasis Chaudhuri , Piotr B. Mucha , Milan Pokorný

In this paper, we study the global well-posedness of a coupled system of kinetic and fluid equations. More precisely, we establish the global existence of weak solutions for Navier-Stokes-BGK system consisting of the BGK model of Boltzmann…

Analysis of PDEs · Mathematics 2018-01-26 Young-Pil Choi , Seok-Bae Yun

We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tensor is monotone satisfying a power-law growth with power $r$…

Analysis of PDEs · Mathematics 2024-01-11 Cosmin Burtea , Maja Szlenk

We study the Navier-Stokes-Darcy-Boussinesq system that models the thermal convection of a fluid overlying a saturated porous medium in a general decomposed domain. In both two and three spatial dimensions, we first prove the existence of…

Analysis of PDEs · Mathematics 2024-08-21 Xiaoming Wang , Hao Wu

We prove the existence of a weak solution to the compressible Navier--Stokes system with singular pressure that explodes when density achieves its congestion level. This is a quantity whose initial value evolves according to the transport…

Analysis of PDEs · Mathematics 2022-02-09 Milan Pokornyý , Aneta Wróblewska-Kamińska , Ewelina Zatorska

We study the Navier-Stokes system describing the motion of a compressible viscous fluid driven by a nonlinear multiplicative stochastic force. We establish local in time existence (up to a positive stopping time) of a unique solution, which…

Analysis of PDEs · Mathematics 2016-06-20 Dominic Breit , Eduard Feireisl , Martina Hofmanova

In this paper, we consider a two-dimensional non-resistive magnetohydrodynamic model, taking the fluctuation of absolute temperature into account. Combining the method of weak convergence developed by Lions [20], Feireisl et al. [7, 8] from…

Analysis of PDEs · Mathematics 2020-09-15 Yang Li , Yongzhong Sun

In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove compactness of finite energy weak solutions for large initial data. In contrast…

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

We study a Navier-Stokes/Cahn-Hilliard system modeling the evolution of a compressible binary mixture of viscous fluids undergoing phase separation. The novelty of this work is a free energy potential including the physically relevant…

Analysis of PDEs · Mathematics 2025-06-10 Danica Basarić , Andrea Giorgini

In this paper we study a vanishing pressure process for highly compressible Navier-Stokes equations as the Mach number tends to infinity. We first prove the global existence of weak solutions for the pressureless system in the framework…

Analysis of PDEs · Mathematics 2017-11-22 Zhilei Liang

This short paper is an introduction of the memoir recently written by the two authors (see [D.Bresch., P.--E. Jabin, arXiv:1507.04629, (2015)]) which concerns the resolution of two longstanding problems: Global existence of weak solutions…

Analysis of PDEs · Mathematics 2016-05-19 D. Bresch , P. -E. Jabin

We address the global-in-time existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We show the details of the $\alpha$-dependence of different…

Analysis of PDEs · Mathematics 2021-03-30 Anthony Suen

This work concerns the global existence of the weak solutions to a system of partial differential equations modeling the evolution of particles in the fluid. That system is given by a coupling between the standard isentropic compressible…

Analysis of PDEs · Mathematics 2018-06-13 Irene M. Gamba , Cheng Yu

The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper. The existence, uniqueness, and regularity of global weak solution…

Analysis of PDEs · Mathematics 2023-04-07 Hai-Liang Li , Ling-Yun Shou

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

Analysis of PDEs · Mathematics 2015-06-03 Helmut Abels , Daniel Depner , Harald Garcke

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

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 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