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This study investigates the asymptotic behavior of the steady-state quasi-Newtonian Stokesflow with viscosity given by the Carreau law within a thin domain, focusing on the effects of a slightly rough boundary of the domain. Employing…

Analysis of PDEs · Mathematics 2025-08-08 María Anguiano , Francisco J. Suárez-Grau

We study a stochastically perturbed mean curvature flow for graphs in $\mathbb{R}^3$ over the two-dimensional unit-cube subject to periodic boundary conditions. In particular, we establish the existence of a weak martingale solution. The…

Analysis of PDEs · Mathematics 2016-08-22 Martina Hofmanova , Matthias Roeger , Max von Renesse

We exploit a two-dimensional model [7], [6] and [1] describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic…

Analysis of PDEs · Mathematics 2021-07-28 V. Kozlov , S. Nazarov , G. Zavorokhin

We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity. For this problem, the classical finite elements method of degree one converges only to order one-half for the L2 norm of the vorticity. We…

Numerical Analysis · Mathematics 2024-12-16 François Dubois , Michel Salaün , Stéphanie Salmon

We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in $\mathbb{R}^2$. We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a…

Analysis of PDEs · Mathematics 2023-08-09 Yannick Sire , Yantao Wu , Yifu Zhou

This paper is concerned with a shape sensitivity analysis of a viscous incompressible fluid driven by Stokes equations with nonhomogeneous boundary condition. The structure of shape gradient with respect to the shape of the variable domain…

Optimization and Control · Mathematics 2007-05-23 Z. M. Gao , Y. C. Ma , H. W. Zhuang

In this study we are interested in the Navier-Stokes-like system for generalized viscous fluids whose viscosity has a power-structure with exponent q. We develop an existence theory of periodic in time weak solutions to the…

Analysis of PDEs · Mathematics 2023-01-11 Anna Abbatiello

In this paper, we consider the Stokes equations with non-homogeneous free boundary conditions, which is obtained by the linearization procedure of the free boundary problem of the Navier-Stokes equations describing the viscous compressible…

Analysis of PDEs · Mathematics 2025-02-20 Yuko Enomoto , Yoshihiro Shibata

The 2D Euler system, which governs inviscid incompressible fluid flow, can admit infinitely many steady solutions in a given domain with slip boundary conditions. To select physical classical solutions, we investigate the vanishing…

Analysis of PDEs · Mathematics 2026-05-21 Changfeng Gui , Chunjing Xie , Huan Xu

We study the two-phase Stokes flow driven by surface tension with two fluids of equal viscosity, separated by an asymptotically flat interface with graph geometry. The flow is assumed to be two-dimensional with the fluids filling the entire…

Analysis of PDEs · Mathematics 2024-04-26 Bogdan-Vasile Matioc , Georg Prokert

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

We consider the Stokes equations subject to Navier boundary conditions on a two-dimensional wedge domain with opening angle $\theta_0 \in (0,\,\pi)$. We prove existence and uniqueness of solutions with optimal regularity in an…

Analysis of PDEs · Mathematics 2024-11-01 Matthias Köhne , Jürgen Saal , Laura Westermann

The construction of weak solutions to compressible Navier-Stokes equations via a numerical method (including a rigorous proof of the convergence) is in a short supply, and so far, available only for one sole numerical scheme suggested in…

Numerical Analysis · Mathematics 2020-07-06 Young-Sam Kwon , Antonin Novotny

We study the two-phase, horizontally periodic, quasistationary Stokes flow in two dimensions driven by surface tension and gravity effects in the general context of fluids with (possibly) different viscosities and densities. The sharp…

Analysis of PDEs · Mathematics 2025-08-22 Daniel Böhme , Bogdan-Vasile Matioc

Periodic traveling waves are numerically computed in a constant vorticity flow subject to the force of gravity. The Stokes wave problem is formulated via a conformal mapping as a nonlinear pseudo-differential equation, involving a periodic…

Fluid Dynamics · Physics 2018-02-22 Sergey A. Dyachenko , Vera Mikyoung Hur

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

We develop a new boundary condition for the weak inverse mean curvature flow, which gives canonical and non-trivial solutions in bounded domains. Roughly speaking, the boundary of the domain serves as an outer obstacle, and the evolving…

Differential Geometry · Mathematics 2025-02-10 Kai Xu

We study the dynamics of the interface given by two incompressible viscous fluids in the Stokes regime filling a 2D horizontally periodic strip. The fluids are subject to the gravity force and the density difference induces the dynamics of…

Analysis of PDEs · Mathematics 2023-01-03 Francisco Gancedo , Rafael Granero-Belinchón , Elena Salguero

In this paper we treat three problems on a two-dimensional `punctured periodic domain': we take $\Omega_r=(-L,L)^2\setminus D_r$, where $D_r=B(0,r)$ is the disc of radius $r$ centred at the origin. We impose periodic boundary conditions on…

Analysis of PDEs · Mathematics 2017-11-13 Michel Chipot , Jerome Droniou , Gabriela Planas , James C. Robinson , Wei Xue

We consider the Nernst-Planck-Stokes system on a bounded domain of $\mathbb{R}^d$, $d=2,3$ with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. It is well known that, in a wide range of cases, equilibrium…

Analysis of PDEs · Mathematics 2025-01-09 Fizay-Noah Lee