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In this paper, we rigorously justify the incompressible Euler limit of the Boltzmann equation with general Maxwell reflection boundary condition in the half-space. The accommodation coefficient $\alpha \in (0,1]$ is assumed to be $O(1)$.…

Analysis of PDEs · Mathematics 2025-06-24 Ning Jiang , Chao Wang , Yulong Wu , Zhifei Zhang

We address here the discretization of the momentum convection operator for fluid flow simulations on 2D triangular and quadrangular meshes and 3D polyhedral meshes containing hexahedra, tetrahedra, prisms and pyramids. The finite volume…

Numerical Analysis · Mathematics 2022-09-15 Aubin Brunel , Raphaèle Herbin , Jean-Claude Latché

This paper is focused on the approximation of the Euler equations of compressible fluid dynamics on a staggered mesh. With this aim, the flow parameters are described by the velocity, the density and the internal energy. The thermodynamic…

Numerical Analysis · Mathematics 2023-07-20 Rémi Abgrall

We consider the compressible Euler equation with a Coriolis term and prove a lower bound on the time of existence of solutions in terms of the speed of rotation, sound speed and size of the initial data. Along the way, we obtain precise…

Analysis of PDEs · Mathematics 2026-04-13 Haram Ko , Benoit Pausader , Ryo Takada , Klaus Widmayer

A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional…

Analysis of PDEs · Mathematics 2015-07-28 Gui-Qiang G. Chen , Fei-Min Huang , Tian-Yi Wang

We prove the incompressible limit of non-isentropic inviscid elastodynamic equations with general initial data in 3D half-space. The deformation tensor is assumed to satisfy the neo-Hookean linear elasticity and degenerates in the normal…

Analysis of PDEs · Mathematics 2024-12-16 Jiawei Wang , Junyan Zhang

Euler alignment systems appear as hydrodynamic limits of interacting self-propelled particle systems such as the (generalized) Cucker-Smale model. In this work, we study weak solutions to an Euler alignment system on smooth, bounded,…

Analysis of PDEs · Mathematics 2023-05-24 Amoolya Tirumalai , Christos Mavridis , John S. Baras

We consider two distinguished asymptotic limits of the Euler equations in a gravitational field, namely the incompressible and Boussinesq limits. Both these limits can be obtained as singular limits of the Euler equations under appropriate…

Numerical Analysis · Mathematics 2019-02-04 K. R. Arun , S. Samantaray

We investigate the relaxation problem and the diffusion phenomenon for the compressible Euler system with a time-dependent damping coefficient of the form $\tfrac{\mu}{(1+t)^{\lambda}}$ in $\mathbb{R}^d$ $(d \geq 1)$. We establish uniform…

Analysis of PDEs · Mathematics 2025-12-09 Timothée Crin-Barat , Xinghong Pan , Ling-Yun Shou , Qimeng Zhu

We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of…

Analysis of PDEs · Mathematics 2025-08-26 Piotr B. Mucha , Sarka Necasova , Maja Szlenk

We show that any dissipative (measure-valued) solution of the compressible Euler system that complies with Dafermos' criterion of maximal dissipation is necessarily an admissible weak solution. In addition, we propose a simple, at most two…

Analysis of PDEs · Mathematics 2025-01-23 Eduard Feireisl , Ansgar Jüngel , Mária Lukáčová-Medvid'ová

We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by large boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime…

Analysis of PDEs · Mathematics 2023-04-04 Eduard Feireisl , Piotr Gwiazda , Young-Sam Kwon , Agnieszka Świerczewska-Gwiazda

The goal of this note is to show that, also in a bounded domain $\Omega \subset \mathbb{R}^n$, with $\partial \Omega\in C^2$, any weak solution, $(u(x,t),p(x,t))$, of the Euler equations of ideal incompressible fluid in $\Omega\times (0,T)…

Analysis of PDEs · Mathematics 2017-12-06 Claude Bardos , Edriss S. Titi

We consider the asymptotic behavior of compressible isentropic flow when the initial mass is finite, which is modeled by the compressible Euler equation with frictional damping. It is shown in \cite{HUA} (resp.\cite{GEN}) that any…

Analysis of PDEs · Mathematics 2024-08-27 Jun-Ren Luo , Ti-Jun Xiao

In the present thesis, we are interested in the description of the dynamics of flows on large scales. In this context, the fluids are governed by rotational, weak compressibility and stratification effects, whose importance is measured by…

Analysis of PDEs · Mathematics 2022-05-25 Gabriele Sbaiz

In this paper, we consider the Cauchy problem for a compressible Oldroyd-B model in three dimensions. Under some smallness assumptions on the initial data, we obtain the global wellposedness of strong solution with uniform regularity.…

Analysis of PDEs · Mathematics 2022-04-07 Sili Liu , Yingshan Chen

The motion of a compressible inviscid radiative flow can be described by the radiative Euler equations, which consists of the Euler system coupled with a Poisson equation for the radiative heat flux through the energy equation. Although…

Analysis of PDEs · Mathematics 2024-09-24 Huijiang Zhao , Boran Zhu

We show that for any $\gamma < \frac{1}{3}$ there exist H\"{o}lder continuous weak solutions $v \in C^{\gamma}([0,T] \times \mathbb{T}^2)$ of the two-dimensional incompressible Euler equations that strictly dissipate the total kinetic…

Analysis of PDEs · Mathematics 2025-11-18 Lili Du , Xinliang Li , Weikui Ye

In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $1<\gamma\leq 3$, by constructing some new control functions ingeniously, we obtain the lower bounds estimates…

Analysis of PDEs · Mathematics 2022-01-21 Ying Sui , Weiqiang Wang , Huimin Yu

We prove the existence of infinitely many mixing solutions for the Muskat problem in the fully unstable regime displaying a linearly degraded macroscopic behaviour inside the mixing zone. In fact, we estimate the volume proportion of each…

Analysis of PDEs · Mathematics 2018-05-31 Ángel Castro , Daniel Faraco , Francisco Mengual