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Related papers: The Mean-Field Limit for Solid Particles in a Navi…

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We consider the flow of a viscous, incompressible, Newtonian fluid in a perforated domain in the plane. The domain is the exterior of a regular lattice of rigid particles. We study the simultaneous limit of vanishing particle size and…

Analysis of PDEs · Mathematics 2015-08-31 Christophe Lacave , Anna Mazzucato

We consider a microscopic model of spherical particles with inertia in a Stokes flow. As the particle number grows to infinity and their size goes to zero we derive the monokinetic Vlasov-Stokes equations as mean-field limit. We do this…

Analysis of PDEs · Mathematics 2025-11-19 Richard M. Höfer , A. Mecherbet , R. Schubert

This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…

Analysis of PDEs · Mathematics 2013-11-25 J. A. Carrillo , Y. -P. Choi , T. K. Karper

We study a generalization of the Navier-Stokes-Fourier system for an incompressible fluid where the deviatoric part of the Cauchy stress tensor is related to the symmetric part of the velocity gradient via a maximal monotone 2-graph that is…

Analysis of PDEs · Mathematics 2017-05-02 Erika Maringová , Josef Žabenský

The description of a stellar system as a continuous fluid represents a convenient first approximation to stellar dynamics, and its derivation from the kinetic theory is standard. The challenge lies in providing adequate closure…

Astrophysics · Physics 2007-05-23 Edward A. Spiegel , Jean-Luc Thiffeault

The general concern of this paper is the effect of rough boundaries on fluids. We consider a stationary flow, governed by incompressible Navier-Stokes equations, in an infinite domain bounded by two horizontal rough plates. The roughness is…

Analysis of PDEs · Mathematics 2007-05-23 Arnaud Basson , David Gerard-Varet

We consider the sedimentation of $N$ spherical particles with identical radii $R$ in a Stokes flow in $\mathbb R^3$. The particles satisfy a no-slip boundary condition and are subject to constant gravity. The dynamics of the particles is…

Analysis of PDEs · Mathematics 2025-01-10 Richard M. Höfer , Richard Schubert

We discuss the flow field and propulsion velocity of active droplets, which are driven by body forces residing on a rigid gel. The latter is modelled as a porous medium which gives rise to permeation forces. In the simplest model, the…

Soft Condensed Matter · Physics 2018-03-26 Reiner Kree , Annette Zippelius

Given an obstacle in $\mathbb{R}^3$ and a non-zero velocity with small amplitude at the infinity, we construct the unique steady Boltzmann solution flowing around such an obstacle with the prescribed velocity as $|x|\to \infty$, which…

Mathematical Physics · Physics 2022-06-07 Raffaele Esposito , Yan Guo , Rossana Marra

The steady motion of a viscous incompressible fluid in a multiply-connected, planar, bounded domain (perforated with a large number of small holes) is modeled through the Navier-Stokes equations with non-homogeneous Dirichlet boundary data…

Analysis of PDEs · Mathematics 2025-02-25 Clara Patriarca , Gianmarco Sperone

Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…

Mathematical Physics · Physics 2018-10-10 Thomas Jankuhn , Maxim A. Olshanskii , Arnold Reusken

We establish the incompressible Navier--Stokes limit for the discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which remain in a suitable small neighborhood of the global Maxwellian.…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 A. Bellouquid

We study incompressible Navier--Stokes flows in~$\R^d$ with small and well localized data and external force~$f$. We establish pointwise estimates for large~$|x|$ of the form \hbox{$c_t|x|^{-d}\le |u(x,t)|\le c'_t|x|^{-d}$}, where $c_t>0$…

Analysis of PDEs · Mathematics 2014-02-25 Hyeong-Ohk Bae , Lorenzo Brandolese

We consider the hydrodynamic limits of the quantum Boltzmann equation with Fermi-Dirac statistics for hard sphere and hard potentials in the whole space. By analyzing the spectrum of the linearized collision operator combined with the…

Analysis of PDEs · Mathematics 2025-09-26 Ning Jiang , Chenchen Wang , Kai Zhou

This paper investigates a modification of the fictitious domain method with continuation in the lower-order coefficients for the unsteady Navier-Stokes equations governing the motion of an incompressible homogeneous fluid in a bounded 2D or…

Numerical Analysis · Mathematics 2025-12-23 Zhanybek Baitulenov , Maxim Olshanskii , Almas Temirbekov , Nurlan Temirbekov , Syrym Kasenov

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…

We consider the motion of a rigid body, governed by the Navier-Stokes equations in a bounded domain. Navier's condition is prescribed on the boundary of the body. We give the global in a time solvability result of weak solution. The result…

Analysis of PDEs · Mathematics 2017-06-20 Nikolai V. Chemetov , Sarka Necasova

The aim of this work is to study the Navier-Stokes-Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated non-linear initial-and boundary-value problem, we prove the…

Analysis of PDEs · Mathematics 2023-09-04 Hermenegildo Borges de Oliveira , Khonatbek Khompysh , Aidos Ganizhanuly Shakir

We study a coupled fluid-structure system involving boundary conditions on the pressure. The fluid is described by the incompressible Navier--Stokes equations in a 2D rectangular type domain where the upper part of the domain is described…

Analysis of PDEs · Mathematics 2018-05-17 Jean-Jérôme Casanova

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in $\R^3$ with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the…

Analysis of PDEs · Mathematics 2009-01-05 Gui-Qiang Chen , Zhongmin Qian