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The stationary Navier--Stokes--Cahn--Hilliard equations are considered, governing the motion of a compressible, two-phase fluid mixture with a diffuse interface. The free energy density in this paper has a singular logarithmic…

Analysis of PDEs · Mathematics 2026-05-05 Zhilei Liang , Sen Liu , Jiangyu Shuai , Dehua Wang

This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole $\mathbb{R}^3$. The fluid is modelled by the incompressible nonhomogeneous…

Analysis of PDEs · Mathematics 2019-10-14 Sarka Necasova , Mythily Ramaswamy , Arnab Roy , Anja Schlomerkemper

A self-consistent saturation model for the prediction of aeroacoustic limit cycles emerging in turbulent low-Mach cavity flows (Re=O(10^5), M\simeq 0.2) is proposed. It predicts the nonlinear interactions between the acoustic modes of a…

Fluid Dynamics · Physics 2025-09-23 Nikolaos Bozikis , Dilara Özev , Nicolas Noiray

In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are perturbations of annular equilibria, in contrast to the laminar…

Analysis of PDEs · Mathematics 2026-04-14 Changfeng Gui , Jun Wang , Wen Yang , Yong Zhang

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

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

Quasi-stationary, or metastable, states play an important role in two-dimensional turbulent fluid flows where they often emerge on time-scales much shorter than the viscous time scale, and then dominate the dynamics for very long time…

Analysis of PDEs · Mathematics 2012-05-18 Margaret Beck , C. Eugene Wayne

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

This paper investigates the asymptotic stability of rarefaction waves for a one-dimensional compressible fluid system, where the Newton's law of viscosity and Fourier's law of heat conduction are replaced by Maxwell's law and Cattaneo's…

Analysis of PDEs · Mathematics 2026-01-21 Yuxi Hu , Mengran Yuan , Jie Zhang

In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In…

The steady state of a forced Taylor-Green flow is investigated in a rotating frame of reference. The investigation involves the results of 184 numerical simulations for different Reynolds number $\mathrm{Re}_{_{F}}$ and Rossby number…

Fluid Dynamics · Physics 2015-06-22 Alexandros Alexakis

We prove the conservation of energy for weak and statistical solutions of the two-dimensional Euler equations, generated as strong (in an appropriate topology) limits of the underlying Navier-Stokes equations and a Monte Carlo-Spectral…

Analysis of PDEs · Mathematics 2021-02-25 S. Lanthaler , S. Mishra , C. Parés-Pulido

The asymptotic limit of the 2D and 3D Navier-Stokes-Korteweg system for barotropic capillary fluids with density dependent viscosities in the low Mach number and vanishing viscosity regime is established. In the relative energy framework,…

Analysis of PDEs · Mathematics 2025-07-03 Matteo Caggio , Donatella Donatelli , Lars Eric Hientzsch

Adding some nontrivial terms composed from a microstructure, we prove the existence of a global-in-time weak solution, whose enstrophy is bounded for all the time, to an incompressible 3D Navier-Stokes-Fourier system for arbitrary initial…

Analysis of PDEs · Mathematics 2024-05-24 Zhongyang Gu , Xin Hu , Tsuyoshi Yoneda

The fluid dynamic limit of the Boltzmann equation leading to the Euler equations for an incompressible fluid with constant density in the presence of material boundaries shares some important features with the better known inviscid limit of…

Analysis of PDEs · Mathematics 2013-05-01 François Golse

Some turbulent flows self-organize into large-scale structures, rather than breaking up into ever-smaller scales. Underpinning this phenomenon is the existence of two sign-definite quantities which are conserved by the dynamics.…

Fluid Dynamics · Physics 2026-02-26 Anna Frishman , Sébastien Gomé , Anton Svirsky

We investigate the time-asymptotic stability of solutions to the one-dimensional Navier-Stokes-Fourier system in the half-space, focusing on the outflow and impermeable wall problems. When the prescribed boundary and far-field conditions…

Analysis of PDEs · Mathematics 2026-03-03 Xushan Huang , Hobin Lee , HyeonSeop Oh

An effort has been made to solve the Cauchy problem of the Navier-Stokes equations in the whole space by two methods. It is proved that the sum of the three vorticity components is a time-invariant in fluid motion. It has been proved that,…

Fluid Dynamics · Physics 2014-09-18 F. Lam

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

We present measurements of relativistic scaling relations in $(2+1)$-dimensional conformal fluid turbulence from direct numerical simulations, in the weakly compressible regime. These relations were analytically derived previously in…

High Energy Physics - Theory · Physics 2017-09-13 John Ryan Westernacher-Schneider , Luis Lehner