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A full viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential coupled with a Poisson equation in one dimensional bounded intervals is studied. First, the existence and…

Analysis of PDEs · Mathematics 2023-07-03 Xiaoying Han , Yuming Qin , Wenlong Sun

The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. We focus on the case of a sharply aligned…

Soft Condensed Matter · Physics 2025-07-29 Tanumoy Dhar , Michael J. Shelley , David Saintillan

We investigate a new two-dimensional compressible Navier-Stokes hydrodynamic model design to explain and study large scale ice swirls formation at the surface of the ocean. The linearized model generates a basis of Bessel solutions from…

Pattern Formation and Solitons · Physics 2019-07-24 Zhi Zong , Andrei Ludu

We study a coupled fluid-structure system involving boundary conditions on the pressure. The fluid is described by the incompressible Navier--Stokes equations in a 2D rectangular type domain where the upper part of the domain is described…

Analysis of PDEs · Mathematics 2018-05-17 Jean-Jérôme Casanova

In this paper we study obstacles immerged in a Stokes flow with Navier boundary conditions. We prove the existence and regularity of an obstacle with minimal drag, among all shapes of prescribed volume and controlled surface area, taking…

Analysis of PDEs · Mathematics 2023-01-04 Dorin Bucur , Antonin Chambolle , Alessandro Giacomini , Mickaël Nahon

We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the…

Analysis of PDEs · Mathematics 2022-06-08 Miroslav Bulíček , Josef Málek , Casey Rodriguez

We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of…

Analysis of PDEs · Mathematics 2018-01-17 Mitsuo Higaki , Yasunori Maekawa , Yuu Nakahara

In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations…

Analysis of PDEs · Mathematics 2012-12-18 Jingchi Huang , Marius Paicu , Ping Zhang

A new presentation of general solution of Navier-Stokes equations is considered here. We consider equations of motion for 3-dimensional non-stationary incompressible flow. The field of flow velocity as well as the equation of momentum…

Analysis of PDEs · Mathematics 2015-06-30 Sergey V. Ershkov

In this paper we introduce a finite element method for the Stokes equations with a massless immersed membrane. This membrane applies normal and tangential forces affecting the velocity and pressure of the fluid. Additionally, the points…

Numerical Analysis · Mathematics 2019-05-01 Kyle Dunn , Roger Lui , Marcus Sarkis

We investigate the modes of deformation of an initially spherical bubble immersed in a homogeneous and isotropic turbulent background flow. We perform direct numerical simulations of the two-phase incompressible Navier-Stokes equations,…

Fluid Dynamics · Physics 2021-07-07 Stéphane Perrard , Aliénor Rivière , Wouter Mostert , Luc Deike

A physical model of a three-dimensional flow of a viscous bubbly fluid in an intermediate regime between bubble formation and breakage is presented. The model is based on mechanics and thermodynamics of a single bubble coupled to the…

Fluid Dynamics · Physics 2019-01-08 Ryan J. Thiessen , Alexei F. Cheviakov

Motivated by the dynamics of microbubbles near catalytic surfaces in bubble-powered microrockets, we consider theoretically the growth of a free spherical bubble near a flat no-slip surface in a Stokes flow. The flow at the bubble surface…

Fluid Dynamics · Physics 2018-12-05 Sebastien Michelin , Giacomo Gallino , Francois Gallaire , Eric Lauga

In this paper, we show existence and non-uniqueness on the axially symmetric stationary Navier-Stokes equations in an exterior periodic cylinder. On the boundary of the cylinder, the horizontally swirl velocity is subject to the…

Analysis of PDEs · Mathematics 2025-03-18 Zijin Li , Xinghong Pan

We consider a two-phase problem for two incompressible, viscous and immiscible fluids which are separated by a sharp interface. The problem arises as a sharp interface limit of a diffuse interface model. We present results on local…

Analysis of PDEs · Mathematics 2012-09-17 Helmut Abels , Mathias Wilke

We treat the 1D shock tube problem, establishing existence of steady solutions of full (nonisentropic) polytropic gas dynamics with arbitrary noncharacteristic data. We present also numerical experiments indicating uniqueness and…

Analysis of PDEs · Mathematics 2023-04-13 Blake Barker , Benjamin Melinand , Kevin Zumbrun

The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…

Analysis of PDEs · Mathematics 2017-09-15 Nicolas Seguin

We consider the dynamics of a gas bubble immersed in an incompressible fluid of fixed temperature, and focus on the relaxation of an expanding and contracting spherically symmetric bubble due to thermal effects. We study two models, both…

Analysis of PDEs · Mathematics 2023-10-05 Chen-Chih Lai , Michael I. Weinstein

We study the steady streaming between two infinitely long circular cylinders produced by small amplitude transverse vibrations of the inner cylinder about the axis of the outer cylinder. The Vishik-Lyusternik method is employed to construct…

Fluid Dynamics · Physics 2010-11-24 K. Ilin , M. A. Sadiq

We consider the compressible Navier--Stokes equation in a perturbed half-space with an outflow boundary condition as well as the supersonic condition. For a half-space, it has been known that a certain planar stationary solution exist and…

Analysis of PDEs · Mathematics 2021-11-23 Masahiro Suzuki , Katherine Zhiyuan Zhang