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We initiate the study of noncharacteristic boundary layers in hyperbolic-parabolic problems with Neumann boundary conditions. More generally, we study boundary layers with mixed Dirichlet--Neumann boundary conditions where the number of…

Analysis of PDEs · Mathematics 2012-07-31 Olivier Gues , Guy Metivier , Mark Williams , Kevin Zumbrun

Following the previous part of our study on unsteady non-New\-to\-nian fluid flows with boundary conditions of friction type we consider in this paper the case of pseudo-plastic (shear thinning) fluids. The problem is described by a…

Analysis of PDEs · Mathematics 2021-12-16 Mahdi Boukrouche , Hanene Debbiche , Laetitia Paoli

We present the results of a Direct Numerical Simulation of a particle-laden spatially developing turbulent boundary layer up to Re{\theta} = 2500. Two main features differentiate the behavior of inertial particles in a zero-…

Solving numerically hydrodynamical problems of incompressible fluids raises the question of handling first order derivatives (those of pressure) in a closed container and determining its boundary conditions. We research several pressure…

Analysis of PDEs · Mathematics 2009-11-07 H. Herrero , A. M. Mancho

We investigate a parabolic-elliptic chemotaxis-consumption-growth system with a Robin boundary condition imposed on the signal. First, we analyse the steady state problem, then we show that the solutions of the system are global and…

Analysis of PDEs · Mathematics 2025-04-29 Piotr Knosalla

We consider the Navier-Stokes equation in a domain with irregular boundaries. The irregularity is modeled by a spatially homogeneous random process, with typical size $\eps \ll 1$. In a parent paper, we derived a homogenized boundary…

Analysis of PDEs · Mathematics 2009-11-13 David Gerard-Varet

The chemotaxis-Navier-Stokes system linking the chemotaxis equations \[ n_t + u\cdot\nabla n = \Delta n - \nabla \cdot (n\chi(c)\nabla c) \] and \[ c_t + u\cdot\nabla c = \Delta c-nf(c) \] to the incompressible Navier-Stokes equations, \[…

Analysis of PDEs · Mathematics 2015-06-23 Michael Winkler

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 fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional…

Analysis of PDEs · Mathematics 2009-11-11 A. Sotirov

In this paper, we derive sharp bounds on the semigroup of the linearized incompressible Navier-Stokes equations near a stationary shear layer in the half plane and in the half space ($\mathbb{R}_+^2$ or $\mathbb{R}_+^3$), with Dirichlet…

Analysis of PDEs · Mathematics 2019-12-25 Emmanuel Grenier , Toan T. Nguyen

In this paper, we investigate the incompressible steady Navier-Stokes system with Navier slip boundary condition in a two-dimensional channel. As long as the width of cross-section of the channel grows more slowly than the linear growth,…

Analysis of PDEs · Mathematics 2022-11-23 Kaijian Sha , Yun Wang , Chunjing Xie

We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The…

Analysis of PDEs · Mathematics 2020-02-17 Sunčica Čanić , Marija Galić , Boris Muha

This article deals with an initial-boundary value problem for the coupled chemotaxis-haptotaxis system with nonlinear diffusion \begin{align*} u_t=&\nabla\cdot(D(u)\nabla u)-\chi\nabla\cdot(u\nabla v)-\xi\nabla\cdot(u\nabla w)+\mu…

Analysis of PDEs · Mathematics 2016-04-20 Yan Li , Johannes Lankeit

In this paper we study the regularity problem of a three dimensional chemotaxis-Navier-Stokes system on a periodic domain. A new regularity criterion in terms of only low modes of the oxygen concentration and the fluid velocity is obtained…

Analysis of PDEs · Mathematics 2018-05-22 Mimi Dai , Han Liu

This work is devoted to the problem of boundary stabilization of a mixture of two viscous and incompressible fluids in a three dimensional channel-like domain $(x,y,z)\in \mathbb{R}\times (0,1)\times\mathbb{R}$. The model consists of the…

Optimization and Control · Mathematics 2020-11-19 Ionut Munteanu

The existence of weak solutions to the Navier-Stokes-Fourier system describing the stationary states of a compressible, viscous, and heat conducting fluid in bounded 2D-domains is shown under fairly general and physically relevant…

Analysis of PDEs · Mathematics 2019-02-28 I. S. Ciuperca , E. Feireisl , M. Jai , A. Petrov

In this paper, we establish the vanishing viscosity limit result of the 2D stationary Navier-Stokes equations outside a rotating disc. On the boundary of the disc, the fluid is subjected to a small perturbation of a non zero rotation of…

Analysis of PDEs · Mathematics 2025-11-26 Xinghong Pan , Jianfeng Zhao

We prove the existence of a weak solution to the compressible Navier--Stokes system with singular pressure that explodes when density achieves its congestion level. This is a quantity whose initial value evolves according to the transport…

Analysis of PDEs · Mathematics 2022-02-09 Milan Pokornyý , Aneta Wróblewska-Kamińska , Ewelina Zatorska

This work concerns with boundary conditions (BCs) of the linearized moment system for rarefied gases. As the Knudsen number is sufficiently small, we analyze the boundary-layer behaviors of the moment system by resorting to a three-scale…

Analysis of PDEs · Mathematics 2023-06-14 Ruo Li , Yichen Yang , Yizhou Zhou

We consider a chemotaxis-fluid system in the whole plane $\mathbb{R}^{2}$ which describes the motion of bacteria suspended in a Navier-Stokes fluid and attracted by a chemical (oxygen). Employing the vorticity formulation for the fluid…

Analysis of PDEs · Mathematics 2024-08-27 Lucas C. F. Ferreira , Daniel P. A. Lima