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Related papers: On weak solutions to the compressible inviscid two…

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We concern with the global existence and large time behavior of compressible fluids (including the inviscid gases, viscid gases, and Boltzmann gases) in an infinitely expanding ball. Such a problem is one of the interesting models in…

Analysis of PDEs · Mathematics 2018-09-26 Gang Xu , Huicheng Yin

This paper is dedicated to the global existence and optimal decay estimates of strong solutions to the compressible viscoelastic flows in the whole space $\mathbb{R}^n$ with any $n\geq2$. We aim at extending those works by Qian \& Zhang and…

Analysis of PDEs · Mathematics 2022-08-08 Xinghong Pan , Jiang Xu

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

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

In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…

Analysis of PDEs · Mathematics 2025-03-06 Yinghua Li , Wenlin Ye

The present paper deals with the Cauchy problem of a multi-dimensional non-conservative viscous compressible two-fluid system. We first study the well-posedness of the model in spaces with critical regularity indices with respect to the…

Analysis of PDEs · Mathematics 2020-10-20 Fuyi Xu , Meiling Chi , Lishan Liu , Yonghong Wu

This paper concerns the global-in-time evolution of a generic compressible two-fluid model in $\mathbb{R}^d$ ($d\geq3$) with the common pressure law. Due to the non-dissipative properties for densities and two different particle paths…

Analysis of PDEs · Mathematics 2025-02-11 Ling-Yun Shou , Jiayan Wu , Lei Yao , Yinghui Zhang

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

This paper concerns with the compressible two-fluid model with algebraic pressure closure. We prove a conditional weak-strong uniqueness principle, meaning that a finite energy weak solution, with bounded densities, coincides with the…

Analysis of PDEs · Mathematics 2021-12-02 Yang Li , Ewelina Zatorska

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

We prove the global existence of weak solutions to the Navier-Stokes equations of compressible heat-conducting fluids in two spatial dimensions with initial data and external forces which are large and spherically symmetric. The solutions…

Analysis of PDEs · Mathematics 2012-05-01 Fei Jiang , Song Jiang , Junpin Yin

We consider a two-dimensional MHD model describing the evolution of viscous, compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity. Existence of global weak solutions is established…

Analysis of PDEs · Mathematics 2019-07-02 Yang Li , Yongzhong Sun

For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk…

Analysis of PDEs · Mathematics 2025-07-03 Qinghao Lei , Chengfeng Xiong

In dimension $n=2$ and $3$, we show that for any initial datum belonging to a dense subset of the energy space, there exist infinitely many global-in-time admissible weak solutions to the isentropic Euler system whenever $1<\gamma\leq…

Analysis of PDEs · Mathematics 2021-03-09 Robin Ming Chen , Alexis F. Vasseur , Cheng Yu

The continuity of the kinetic energy is an important property of incompressible viscous fluid flows. We show that for any prescribed finite energy divergence-free initial data there exist infinitely many global in time weak solutions with…

Analysis of PDEs · Mathematics 2024-07-25 Alexey Cheskidov , Zirong Zeng , Deng Zhang

We prove existence of global in time weak solutions to a compressible two-fluid Stokes system with a single velocity field and algebraic closure for the pressure law. The constitutive relation involves densities of both fluids through an…

Analysis of PDEs · Mathematics 2018-12-05 Didier Bresch , Piotr B. Mucha , Ewelina Zatorska

We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…

Analysis of PDEs · Mathematics 2014-01-15 Michela Eleuteri , Elisabetta Rocca , Giulio Schimperna

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 show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…

Analysis of PDEs · Mathematics 2024-08-15 Helmut Abels , Harald Garcke , Andrea Poiatti

An initial-and boundary-value problem for the Kelvin-Voigt system, modeling a mixture of n incompressible and viscoelastic fluids, with non-constant density, is investigated in this work. The existence of global-in-time weak solutions is…

Analysis of PDEs · Mathematics 2025-06-13 S. N. Antontsev , H. B. de Oliveira , I. V. Kuznetsov , D. A. Prokudin , Kh. Khompysh