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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

This paper is concerned with the existence of global-in-time weak solutions to the multicomponent reactive flows inside a moving domain whose shape in time is prescribed. The flow is governed by the 3D compressible Navier-Stokes-Fourier…

Analysis of PDEs · Mathematics 2024-07-03 Kuntal Bhandari , Stanislav Kračmar , Šárka Nečasová , Minsuk Yang

This article studies the uniqueness of the weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case. Here, the investigation is provided using two different approaches. The first (the main) result is obtained…

Analysis of PDEs · Mathematics 2024-05-20 Kamal N. Soltanov

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 consider the Cauchy problem for the three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering the system as an elliptic-dominated structure and defining suitable…

Analysis of PDEs · Mathematics 2024-08-09 Xiangdi Huang , Jiaxu Li , Rong Zhang

In this study, we investigate the incompressible generalised Navier-Stokes-Voigt equations within a bounded domain $\Omega \subset \mathbb{R}^d$, where $d \geq 2$. The governing momentum equation is expressed as: $$…

Analysis of PDEs · Mathematics 2026-04-01 Ankit Kumar , Hermenegildo Borges de Oliveira , Manil T. Mohan

This paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform with respect to the Planck constant. This allows…

Analysis of PDEs · Mathematics 2016-07-25 Ingrid Lacroix-Violet , Alexis Vasseur

We show the existence of weak solutions to the fluid-structure interaction problem of a largely deforming viscoelastic bulk solid with a viscous fluid governed by the incompressible Navier-Stokes equations. In contrast to previous works,…

Analysis of PDEs · Mathematics 2026-03-13 Antonín Češík , Malte Kampschulte , Sebastian Schwarzacher

We study the global existence of a unique strong solution and its large-time behavior of a two-phase fluid system consisting of the compressible isothermal Euler equations coupled with compressible isentropic Navier-Stokes equations through…

Analysis of PDEs · Mathematics 2016-07-04 Young-Pil Choi

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

In this paper, we prove the existence of global weak solutions for 3D compressible Navier-Stokes equations with degenerate viscosity. The method is based on the Bresch and Desjardins entropy conservation. The main contribution of this paper…

Analysis of PDEs · Mathematics 2016-12-21 Alexis F. Vasseur , Cheng Yu

We consider the compressible Navier-Stokes-Fourier system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. Assuming that the pressure can be decomposed into an…

Analysis of PDEs · Mathematics 2015-11-17 Ondrej Kreml , Vaclav Macha , Sarka Necasova , Aneta Wroblewska-Kaminska

We investigate uniqueness of weak solutions for a system of partial differential equations capturing behavior of magnetoelastic materials. This system couples the Navier-Stokes equations with evolutionary equations for the deformation…

Analysis of PDEs · Mathematics 2018-06-13 Anja Schlömerkemper , Josef Žabenský

A coupled kinetic-fluid model is investigated, which describes the dynamic behavior of an ensemble of Cucker-Smale flocking particles interacting with a viscous fluid in a three-dimensional bounded domain. This system consists of a kinetic…

Analysis of PDEs · Mathematics 2022-12-06 Li Chen , Yue Li , Nicola Zamponi

We are concerned with the three dimensional incompressible Navier--Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initial condition in $L^{2}$ we establish existence of infinitely…

Probability · Mathematics 2022-02-22 Martina Hofmanová , Rongchan Zhu , Xiangchan Zhu

This paper investigates the global dynamics of a three-dimensional fluid-particle interaction system that couples the compressible barotropic Navier-Stokes equations with the Vlasov-Fokker-Planck equation through a density-dependent…

Analysis of PDEs · Mathematics 2026-03-10 Fucai Li , Jinkai Ni , Dehua Wang

This article is devoted to the well-posedness of the stochastic compressible Navier Stokes equations. We establish the global existence of an appropriate class of weak solutions emanating from large inital data, set within a bounded domain.…

Analysis of PDEs · Mathematics 2015-04-07 Scott Smith

We show the existence of global weak solutions of the 3D Navier-Stokes equations with initial velocity in the weighted spaces L 2 w$\gamma$ , where w $\gamma$ (x) = (1 + |x|) --$\gamma$ and 0 < $\gamma$ $\le$ 2, using new energy controls.…

Analysis of PDEs · Mathematics 2020-04-22 Pedro Gabriel Fernández-Dalgo , Pierre Gilles Lemarié-Rieusset

In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…

Analysis of PDEs · Mathematics 2016-07-15 Šimon Axmann , Piotr B. Mucha , Milan Pokorný

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