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In this paper, we study a hydrodynamic phase-field system modeling the deformation of functionalized membranes in incompressible viscous fluids. The governing PDE system consists of the Navier-Stokes equations coupled with a convective…

Analysis of PDEs · Mathematics 2022-06-22 Hao Wu , Yuchen Yang

It is well-known that liquid and saturated vapor, separated by a flat interface in an unbounded space, are in equilibrium. One would similarly expect a liquid drop, sitting on a flat substrate, to be in equilibrium with the vapor…

Soft Condensed Matter · Physics 2021-09-29 E. S. Benilov

The large deformations and break up of circular 2D liquid patches in a high Reynolds number (Re=1000) gas flow are investigated numerically. The 2D, plane flow Navier--Stokes equations are directly solved with explicit tracking of the…

chao-dyn · Physics 2009-10-28 S. Zaleski , Jie Li , S. Succi

Here we consider a Cahn-Hilliard-Navier-Stokes system characterized by a nonlocal Cahn-Hilliard equation with a singular (e.g., logarithmic) potential. This system originates from a diffuse interface model for incompressible isothermal…

Analysis of PDEs · Mathematics 2012-01-31 Sergio Frigeri , Maurizio Grasselli

The Cahn-Hilliard-Navier-Stokes (CHNS) system utilizes a diffusive phase-field for interface tracking of multi-phase fluid flows. Recently structure preserving methods for CHNS have moved into focus to construct numerical schemes that, for…

Numerical Analysis · Mathematics 2026-04-02 Jimmy Kornelije Gunnarsson , Robert Klöfkorn

We investigate pump-driven droplet electrohydrodynamics with an emphasis on deformation, pinch-off, and recoalescence. A thermodynamically consistent phase-field framework is developed that couples Nernst--Planck--Poisson electrodiffusion…

Fluid Dynamics · Physics 2025-09-15 Yuzhe Qin , Huaxiong Huang , Zilong Song , Shixin Xu

The two-phase Navier-Stokes Cahn-Hilliard (NSCH) mixture model is a key framework for simulating multiphase flows with non-matching densities. Developing fully discrete, energy-stable schemes for this model remains challenging, due to the…

Numerical Analysis · Mathematics 2026-02-05 Aaron Brunk , Marco F. P. ten Eikelder

Cahn-Hilliard-Navier-Stokes (CHNS) systems describes flows with two-phases, e.g., a liquid with bubbles. Obtaining constitutive relations for general dissipative processes for such a systems, which are thermodynamically consistent, can be a…

Mathematical Physics · Physics 2024-10-01 Azeddine Zaidni , Philip J Morrison , Saad Benjelloun

This paper is concerned with the distributed optimal control of a time-discrete Cahn--Hilliard/Navier--Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a family…

Analysis of PDEs · Mathematics 2015-06-12 Michael Hintermüller , Tobias Keil , Donat Wegner

The evolution of two partially miscible, nonhomogeneous, incompressible viscous fluids of non-Newtonian type, can be governed by the Navier-Stokes-Cahn-Hilliard system. In the present work, we prove the global existence of weak solutions…

Analysis of PDEs · Mathematics 2025-12-25 Fang Li , Duan Xingyu , Guo Zhenhua

We prove a priori estimates for the system of partial differential equations modeling the interaction between an elastic body and an incompressible fluid in a 3D curved domain. The fluid is governed by the incompressible Navier-Stokes…

Analysis of PDEs · Mathematics 2026-01-21 B. Ingimarson , I. Kukavica , W. S. Ożański

We derive and analyze a new diffuse interface model for incompressible, viscous fluid mixtures with bulk-surface interaction. Our system consists of a Navier--Stokes--Cahn--Hilliard model in the bulk that is coupled to a surface…

Analysis of PDEs · Mathematics 2025-09-16 Patrik Knopf , Jonas Stange

We consider a diffuse interface model for an incompressible isothermal mixture of two viscous Newtonian fluids with different densities in a bounded domain in two or three space dimensions. The model is the nonlocal version of the one…

Analysis of PDEs · Mathematics 2015-06-01 Sergio Frigeri

We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…

Numerical Analysis · Mathematics 2022-01-19 Nils Margenberg , Thomas Richter

This paper is based on a formulation of the Navier-Stokes equations developed by P. Constantin and the first author (\texttt{arxiv:math.PR/0511067}, to appear), where the velocity field of a viscous incompressible fluid is written as the…

Probability · Mathematics 2010-03-16 Gautam Iyer , Jonathan Mattingly

We consider the interaction of a compressible fluid with a flexible plate in two space dimensions. The fluid is described by the Navier--Stokes equations in a domain that is changing in accordance with the motion of the structure. The…

Analysis of PDEs · Mathematics 2024-11-05 Dominic Breit , Arnab Roy

The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…

Chaotic Dynamics · Physics 2018-08-01 Balachandra Suri , Jeffrey Tithof , Roman O. Grigoriev , Michael F. Schatz

We study in this paper the movement of a rigid solid inside an incompressible Navier-Stokes flow, within a bounded domain. We consider the case where slip is allowed at the fluid/solid interface, through a Navier condition. Taking into…

Analysis of PDEs · Mathematics 2014-03-06 David Gérard-Varet , Matthieu Hillairet

We investigate the well-posedness of the periodic boundary value problem for the steady compressible isentropic Navier-Stokes system under the van der Waals equation of state. The main difficulty arises from the non-monotonicity of the…

Analysis of PDEs · Mathematics 2026-02-18 Yazhou Chen , Qiaolin He , Dongjuan Niu , Yi Peng , Xiaoding Shi

The interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations, coupled to one another along the moving material interface through the continuity of the velocity and traction…

Analysis of PDEs · Mathematics 2009-11-11 Daniel Coutand , Steve Shkoller