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We study the stationary Navier--Stokes equations in the whole plane with a compactly supported force term and with a prescribed constant spatial limit. Prior to this work, existence of solutions to this problem was only known under special…

Analysis of PDEs · Mathematics 2022-11-18 Julien Guillod , Mikhail Korobkov , Xiao Ren

The energy equalities of compressible Navier-Stokes equations with general pressure law and degenerate viscosities are studied. By using a unified approach, we give sufficient conditions on the regularity of weak solutions for these…

Analysis of PDEs · Mathematics 2020-01-08 Quoc-Hung Nguyen , Phuoc-Tai Nguyen , Quoc Bao Tang

We give a uniform bound from below on the temperature for a variant of the compressible Navier-Stokes-Fourier system, under suitable hypotheses. This system of equations forms a mathematical model of the motion of a compressible fluid…

Analysis of PDEs · Mathematics 2014-11-06 Eric Baer , Alexis Vasseur

We study an initial and boundary value problem modelling the motion of a rigid body in a heat conducting gas. The solid is supposed to be a perfect thermal insulator. The gas is described by the compressible Navier-Stokes-Fourier equations,…

Analysis of PDEs · Mathematics 2017-10-24 Bernhard H. Haak , Debayan Maity , Takéo Takahashi , Marius Tucsnak

Due to computational complexity, fluid flow problems are mostly defined on a bounded domain. Hence, capturing fluid outflow calls for imposing an appropriate condition on the boundary where the said outflow is prescribed. Usually, the…

Analysis of PDEs · Mathematics 2021-09-22 John Sebastian H. Simon , Hirofumi Notsu

The incompressible Navier-Stokes equations are re-formulated to involve an arbitrary time dilation; and in this manner, the modified Navier-Stokes equations are obtained which have some penalization terms in the right hand side. Then, the…

Fluid Dynamics · Physics 2014-12-17 Fereidoun Sabetghadam

We investigate the steady self-propelled motion of a rigid body immersed in a three-dimensional incompressible viscous fluid governed by the Navier-Stokes equations. The analysis is performed in a body-fixed reference frame, so that the…

Analysis of PDEs · Mathematics 2026-01-01 Sarka Necasova , Arnab Roy , Ana Leonor Silvestre

A hyperbolic relaxation of the classical Navier-Stokes problem in 2D bounded domain with Dirichlet boundary conditions is considered. It is proved that this relaxed problem possesses a global strong solution if the relaxation parameter is…

Analysis of PDEs · Mathematics 2018-08-01 Alexei Ilyin , Yuri Rykov , Sergey Zelik

The article is devoted to the mathematical analysis of a fluid-structure interaction system where the fluid is compressible and heat conducting and where the structure is deformable and located on a part of the boundary of the fluid domain.…

Analysis of PDEs · Mathematics 2021-05-26 Debayan Maity , Takéo Takahashi

A constraint penalization method is introduced within the Lattice Boltzmann (LBM) framework to model fluid-structure interactions involving rigid bodies. The proposed approach extends the fictitious domain concept by enforcing the…

Fluid Dynamics · Physics 2025-11-04 Tristan Millet , Erwan Liberge

We present and analyze a penalization method wich extends the the method of [1] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow with an interface…

Analysis of PDEs · Mathematics 2009-01-15 Claire Bost , Georges-Henri Cottet , Emmanuel Maitre

We consider the Navier-Stokes-Fourier system with the inhomogeneous boundary conditions for the velocity and the temperature. We show that solutions emanating from sufficiently regular data remain regular as long as the density $\varrho$,…

Analysis of PDEs · Mathematics 2023-02-01 Danica Basarić , Eduard Feireisl , Hana Mizerová

We study traveling wave solutions to the free boundary problem associated to a generalized Navier-Stokes Fourier system, which models a viscous, incompressible, heat-conducting fluid. The fluid is assumed to occupy a horizontally infinite…

Analysis of PDEs · Mathematics 2026-03-24 Jae Ho Choi , Ian Tice

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

We consider the motion of a rigid body immersed in a two-dimensional viscous incompressible fluid with Navierslip-with-friction conditions at the solid boundary. The fluid-solid system occupies the whole plane. We provethe small-time exact…

Analysis of PDEs · Mathematics 2018-07-19 József Kolumbán

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…

Penalty methods relax the incompressibility condition and uncouple velocity and pressure. Experience with them indicates that the velocity error is sensitive to the choice of penalty parameter $\epsilon$. So far, there is no effective \'a…

Numerical Analysis · Mathematics 2024-04-19 Rui Fang

The purpose of this article is to study the convergence of a low order finite element approximation for a natural convection problem. We prove that the discretization based on P1 polynomials for every variable (velocity, pressure and…

Numerical Analysis · Mathematics 2022-07-27 Ionut Danaila , Francky Luddens , Cécile Legrand

The solution of partial differential equations (PDEs) on complex domains often presents a significant computational challenge by requiring the generation of fitted meshes. The Diffuse Domain Method (DDM) is an alternative which reformulates…

Numerical Analysis · Mathematics 2026-05-13 Luke Benfield , Andreas Dedner

We prove that there exists a strong solution to the Dirichlet boundary value problem for the steady Navier-Stokes equations of a compressible heat-conductive fluid with large external forces in a bounded domain $R^d (d = 2, 3)$, provided…

Analysis of PDEs · Mathematics 2014-08-08 Changsheng Dou , Fei Jiang , Song Jiang , Yong-Fu Yang