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In this paper, we investigate an initial-boundary value problem for a chemotaxis-fluid system in a general bounded regular domain $\Omega \subset \mathbb{R}^N$ ($N\in\{2,3\}$), not necessarily being convex. Thanks to the elementary lemma…

Analysis of PDEs · Mathematics 2023-07-28 Jie Jiang , Hao Wu , Songmu Zheng

We consider a mathematical model coupling the Cahn-Hilliard system for phase separation with an additional equation describing the diffusion process of a chemical quantity whose concentration influences the physical process. The main…

Analysis of PDEs · Mathematics 2025-11-17 Giulio Schimperna , Antonio Segatti

We study asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) elastic plate equation for transversal displacement on a flexible flat part of the…

Analysis of PDEs · Mathematics 2011-09-21 Igor Chueshov , Iryna Ryzhkova

This paper considers the degenerate and singular chemotaxis-Navier--Stokes system with logistic term $n_t + u\cdot\nabla n =\Delta n^m - \chi\nabla\cdot(n\nabla c) + \kappa n -\mu n^2$, $x \in \Omega,\ t>0$, $c_t + u\cdot\nabla c = \Delta c…

Analysis of PDEs · Mathematics 2018-02-27 Shunsuke Kurima , Masaaki Mizukami

In this paper we develop a numerical scheme for approximating a $d$-dimensional chemotaxis-Navier-Stokes system, $d=2,3$, modeling cellular swimming in incompressible fluids. This model describes the chemotaxis-fluid interaction in cases…

In this paper, we are concerned with the following prey-taxis system with fluid surrounding describing by the incompressible Navier-Stokes equations in a bounded domain with smooth boundary. We show that it has global classical solutions…

Analysis of PDEs · Mathematics 2018-11-15 Feng Zefu , Jin Hai-yang , Zhu Changjiang

This paper is framed in a series of studies on attraction-repulsion chemotaxis models combining different effects: nonlinear diffusion and sensitivities and logistic sources, for the dynamics of the cell density, and consumption and/or…

Analysis of PDEs · Mathematics 2023-05-17 Tongxing Li , Silvia Frassu , Giuseppe Viglialoro

A three-dimensional chemotaxis-Navier-Stokes system is considered. It is known that for all suitably regular initial data, a corresponding initial-boundary value problem admits at least one global weak solution which can be obtained as the…

Analysis of PDEs · Mathematics 2015-06-19 Michael Winkler

In this paper, we study the rates of convergence of supposedly given global bounded classical solutions to a two-species chemotaxis-Navier-Stokes system with Lotka-Volterra competitive kinetics. Except in one case where the rate of…

Analysis of PDEs · Mathematics 2018-07-18 Hai-Yang Jin , Tian Xiang

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

We consider a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids with matched constant densities. This model consists of the Navier-Stokes system coupled with a convective nonlocal Cahn-Hilliard equation…

Analysis of PDEs · Mathematics 2014-04-16 Sergio Frigeri , Maurizio Grasselli , Elisabetta Rocca

The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or unbounded boundary. Such a model with a free boundary describes the spreading…

Dynamical Systems · Mathematics 2020-02-11 Lianzhang Bao , Wenxian Shen

We investigate further the existence of solutions to kinetic models of chemotaxis. These are nonlinear transport-scattering equations with a quadratic nonlinearity which have been used to describe the motion of bacteria since the 80's when…

Analysis of PDEs · Mathematics 2007-09-27 Nikolaos Bournaveas , Vincent Calvez , Susana Gutiérrez , Benoît Perthame

This paper investigates the connection between the chemotaxis--Navier--Stokes system with porous medium type nonlinear diffusion and the Hele--Shaw problem in $\mathbb{R}^d$ ($d\geq2$). First, we prove the global-in-time existence of weak…

Analysis of PDEs · Mathematics 2025-06-16 Qingyou He , Ling-Yun Shou , Leyun Wu

The Navier-Stokes-Coriolis system is a simple model for rotating fluids, which allows to study the influence of the Coriolis force on the dynamics of three-dimensional flows. In this paper, we consider the NSC system in an infinite…

Analysis of PDEs · Mathematics 2009-01-12 Thierry Gallay , Violaine Roussier-Michon

In this paper, we propose a coupled system describing the interaction between the Relativistic Cucker-Smale model and the incompressible Navier-Stokes equations via a drag force, and establish a global existence theory as well as the…

Analysis of PDEs · Mathematics 2025-03-18 Shenglun Yan , Weiyuan Zou

The present work deals with a Keller-Segel-Navier-Stokes system with potential consumption, under homogeneous Neumann boundary conditions for cell density and chemical signal, and of Dirichlet type for the velocity field, over a bounded…

Analysis of PDEs · Mathematics 2025-06-24 Daniel Barbosa , Gabriela Planas , Francisco Guillén-González

The existence of large-data weak solutions to a steady compressible Navier-Stokes-Fourier system for chemically reacting fluid mixtures is proved. General free energies are considered satisfying some structural assumptions, with a pressure…

Analysis of PDEs · Mathematics 2024-06-19 Miroslav Buliček , Ansgar Jüngel , Milan Pokorný , Nicola Zamponi

The chemotaxis-Navier-Stokes system \begin{equation*}\label{1} \left\{ \begin{array}{rcl} n_t+u\cdot\nabla n &=& \Delta \big(n c^{-\alpha} \big), \\[1mm] c_t+ u\cdot\nabla c &=& \Delta c -nc,\\[1mm] u_t + (u\cdot\nabla) u &=&\Delta u+\nabla…

Analysis of PDEs · Mathematics 2024-10-01 Mario Fuest , Michael Winkler

This paper considers a stochastically perturbed Keller-Segel-Navier-Stokes (KS-SNS) system arising from the biomathematics in two dimensions, where the diffusion of fluid is expressed by a fractional Laplacian with an exponent in $[1/2,1]$.…

Analysis of PDEs · Mathematics 2024-03-12 Lei Zhang , Bin Liu