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We investigate a diffuse-interface model that describes the dynamics of incompressible two-phase viscous flows with surfactant. The resulting system of partial differential equations consists of a sixth-order Cahn-Hilliard equation for the…

Analysis of PDEs · Mathematics 2023-07-28 Andrea Di Primio , Maurizio Grasselli , Hao Wu

We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…

Analysis of PDEs · Mathematics 2017-01-03 Dominic Breit , Martina Hofmanová

In this work we consider the Keller-Segel system coupled with Navier-Stokes equations in $\mathbb{R}^{N}$ for $N\geq2$. We prove the global well-posedness with small initial data in Besov-Morrey spaces. Our initial data class extends…

Analysis of PDEs · Mathematics 2019-07-24 Lucas C. F. Ferreira , Monisse Postigo

We consider the Navier--Stokes equations in a half-plane with a drift term parallel to the boundary and a small source term of compact support. We provide detailed information on the behavior of the velocity and the vorticity at infinity in…

Mathematical Physics · Physics 2012-04-23 Christoph Boeckle , Peter Wittwer

In this paper, we investigate a three-dimensional fluid-particle coupled model. % in whole space $\mathbb{R}^3$. This model combines the full compressible Navier-Stokes equations with the Vlasov-Fokker-Planck equation via the momentum and…

Analysis of PDEs · Mathematics 2024-08-27 Fucai Li , Jinkai Ni , Man Wu

The Cahn-Hilliard-Navier-Stokes system is based on a well-known diffuse interface model and describes the evolution of an incompressible isothermal mixture of binary fluids. A nonlocal variant consists of the Navier-Stokes equations…

Analysis of PDEs · Mathematics 2015-05-30 Sergio Frigeri , Maurizio Grasselli

We analyze the pressureless Navier-Stokes system with nonlocal attraction-repulsion forces. Such systems appear in the context of models of collective behavior. We prove the existence of weak solutions on the whole space $\mathbb{R}^3$ in…

Analysis of PDEs · Mathematics 2024-02-19 Piotr B. Mucha , Maja Szlenk , Ewelina Zatorska

We study the global strong solutions to the compressible Navier-Stokes system with potential temperature transport in $\mathbb{R}^n.$ Different from the Navier-Stokes-Fourier system, the pressure is a nonlinear function of the density and…

Analysis of PDEs · Mathematics 2023-04-04 Xiaoping Zhai , Yongsheng Li , Fujun Zhou

In this paper we consider a coupled hydrodynamical system which involves the Navier-Stokes equations for the velocity field and kinematic transport equations for the molecular orientation field. By applying the Chemin-Lerner's time-space…

Analysis of PDEs · Mathematics 2011-04-22 Jihong Zhao , Qiao Liu , Shangbin Cui

We consider the motion of compressible Navier-Stokes fluids with the hard sphere pressure law around a rigid obstacle when the velocity and the density at infinity are non zero. This kind of pressure model is largely employed in various…

Analysis of PDEs · Mathematics 2022-08-31 Sarka Necasova , Antonin Novotny , Arnab Roy

We consider a diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids. This model consists of the Navier-Stokes equations coupled with a convective nonlocal Cahn-Hilliard equation.…

Analysis of PDEs · Mathematics 2015-09-11 Sergio Frigeri , Ciprian G. Gal , Maurizio Grasselli

A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard…

Analysis of PDEs · Mathematics 2013-01-14 Sergio Frigeri , Maurizio Grasselli , Pavel Krejčí

In this paper, we consider the Cauchy problem of the multi-dimensional compressible Navier-Stokes-Euler system for two-phase flow motion, which consists of the isentropic compressible Navier-Stokes equations and the isothermal compressible…

Analysis of PDEs · Mathematics 2024-08-09 Hai-Liang Li , Ling-Yun Shou

Chemotaxis is a directed cell movement in response to external chemical stimuli. In this paper, we propose a simple model for the origin of chemotaxis - namely how a directed movement in response to an external chemical signal may occur…

Analysis of PDEs · Mathematics 2023-06-30 Yishu Gong , Alexander Kiselev

This article is devoted to the well-posedness of the stochastic compressible Navier Stokes equations. We establish the global existence of an appropriate class of weak solutions emanating from large inital data, set within a bounded domain.…

Analysis of PDEs · Mathematics 2015-04-07 Scott Smith

This paper is concerned with the boundary layer problem on a chemotaxis-Navier-Stokes system modelling the boundary layer formation of aerobic bacteria in fluids. Completing this system with Neumann boundary conditions on oxygen, we show…

Analysis of PDEs · Mathematics 2025-09-04 Qianqian Hou

Based on the global a priori estimates in [Guo-Tice, J. Eur. Math. Soc. (2024)], we establish the well-posedness of a viscous fluid model satisfying the dynamic law for the contact line \begin{equation*}…

Analysis of PDEs · Mathematics 2026-05-12 Yan Guo , Ian Tice , Lei Wu , Xiaoding Yang , Yunrui Zheng

We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that…

Analysis of PDEs · Mathematics 2014-04-08 Peter Bella , Eduard Feireisl , Bum Ja Jin , Antonin Novotny

We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densities and a soluble surfactant in a bounded domain of two or…

Analysis of PDEs · Mathematics 2026-01-13 Bohan Ouyang , Maurizio Grasselli , Hao Wu

The present paper deals with existence and uniqueness of global mild solutions for the 2D Navier-Stokes equations with impulses. Using the framework of nonautonomous dynamical systems, we extend previous results considering the 2D…

Analysis of PDEs · Mathematics 2017-12-06 Everaldo M. Bonotto , Jaqueline G. Mesquita , Ricardo P. Silva