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We consider a loosely coupled algorithm for fluid-structure interaction based on a Robin interface condition for the fluid problem (explicit Robin-Neumann scheme). We study the dependence of the stability of this method on the interface…

Numerical Analysis · Mathematics 2019-05-17 Giacomo Gigante , Christian Vergara

The subject of this article is a matched microstructure model for Newtonian fluid flows in fractured porous media. This is a homogenized model which takes the form of two coupled parabolic differential equations with boundary conditions in…

Analysis of PDEs · Mathematics 2011-12-21 Joachim Escher , Daniela Treutler

The existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and Wiener forcing term is proven. The finite time extinction of solutions with high…

Probability · Mathematics 2018-06-18 Viorel Barbu , Giuseppe Da Prato , Michael Röckner

We introduce a novel monolithic formulation that employs Lagrange multipliers (LMs) to couple a fluid flow governed by the time-dependent Stokes equations with a poroelastic structure described by the Biot equations. The formulation is…

Numerical Analysis · Mathematics 2025-12-10 Amy de Castro , Hyesuk Lee

We consider the interaction between an incompressible, viscous fluid modeled by the dynamic Stokes equation and a multilayered poroelastic structure which consists of a thin, linear, poroelastic plate layer (in direct contact with the free…

Analysis of PDEs · Mathematics 2021-08-17 Lorena Bociu , Sunčica Čanić , Boris Muha , Justin T. Webster

We consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\mathbb{R}^2$ driven by L\'evy noise. Applying the variational approach, global existence and uniqueness of strong probabilistic…

Probability · Mathematics 2017-01-03 Shijie Shang , Jianliang Zhai , Tusheng Zhang

A stationary Stokes problem with a piecewise constant viscosity coefficient in multiple subdomains is considered in the paper. For standard finite element pairs, a robust inf-sup condition is required to show the robustness of the…

Numerical Analysis · Mathematics 2025-07-22 Yuxiang Liang , Shun Zhang

We establish the global well-posedness theory of small BV weak solutions to a one-dimensional compressible Navier--Stokes model for reacting gas mixtures in dynamic combustion. The unknowns of the PDE system consist of the specific volume,…

Analysis of PDEs · Mathematics 2026-02-10 Siran Li , Haitao Wang , Jianing Yang

In this article, we consider the stochastic wave equation on the real line driven by a linear multiplicative Gaussian noise, which is white in time and whose spatial correlation corresponds to that of a fractional Brownian motion with Hurst…

Probability · Mathematics 2016-05-03 Raluca M. Balan , Maria Jolis , Lluís Quer-Sardanyons

We consider the equations of motion for an incompressible Non-Newtonian fluid in a bounded Lipschitz domain $G\subset\mathbb R^d$ during the time intervall $(0,T)$ together with a stochastic perturbation driven by a Brownian motion $W$. The…

Analysis of PDEs · Mathematics 2017-01-11 Dominic Breit

This paper deals with time-fractional stochastic Navier-Stokes equations, which are characterized by the coexistence of stochastic noise and a fractional power of the Laplacian. We establish sufficient conditions for the existence and…

Optimization and Control · Mathematics 2025-10-13 Renu Chaudhary , Simeon Reich , Juan J. Nieto

Stokesian Dynamics (SD) is a numerical framework used for simulating hydrodynamic interactions in particle suspensions at low Reynolds number. It combines far-field approximations with near-field lubrication corrections, offering a balance…

Fluid Dynamics · Physics 2025-03-21 Kim William Torre , Joost de Graaf

We study stochastic differential equations with additive noise and distributional drift on $\mathbb{T}^d$ or $\mathbb{R}^d$ and $d \geqslant 2$. We work in a scaling-supercritical regime using energy solutions and recent ideas for…

Probability · Mathematics 2024-07-15 Lukas Gräfner , Nicolas Perkowski

In this work, we investigate a system of interacting particles governed by a set of stochastic differential equations. Our main goal is to rigorously demonstrate that the empirical measure associated with the particle system converges…

Probability · Mathematics 2025-08-12 Filippo Giovagnini , Dan Crisan

We consider quasi-static poroelastic systems with incompressible constituents. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid…

Analysis of PDEs · Mathematics 2022-02-23 Lorena Bociu , Boris Muha , Justin T. Webster

We analyse a nonlinear stochastic partial differential equation that corresponds to a viscous shallow water equation (of the Camassa--Holm type) perturbed by a convective, position-dependent noise term. We establish the existence of weak…

Analysis of PDEs · Mathematics 2022-11-16 Helge Holden , Kenneth H. Karlsen , Peter H. C. Pang

We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter $H\in (1/2,1)$, and contains a non--trivial coefficient in…

Analysis of PDEs · Mathematics 2014-10-27 Hakima Bessaih , María J. Garrido-Atienza , Björn Schmalfuss

We augment a thermodynamically consistent diffuse interface model for the description of line tension phenomena by multiplicative stochastic noise to capture the effects of thermal fluctuations and establish the existence of pathwise unique…

Numerical Analysis · Mathematics 2025-05-16 Stefan Metzger

We prove the global well-posedness of the one-dimensional Navier-Stokes-Korteweg equations driven by a stochastic multiplicative noise. The analysis is performed for the general case of capillarity and viscosity coefficients $k(\rho)=…

Analysis of PDEs · Mathematics 2026-03-26 L. Pescatore

We construct non-negative martingale solutions to the stochastic porous medium equation in one dimension with homogeneous Dirichlet boundary conditions which exhibit a type of sticky behavior at zero. The construction uses the stochastic…

Probability · Mathematics 2024-11-12 Ben Hambly , Dörte Kreher , Konstantins Starovoitovs