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We study the local well-posedness for an interface with surface tension that separates a perfectly conducting inviscid fluid from a vacuum. The fluid flow is governed by the equations of three-dimensional ideal compressible…

Analysis of PDEs · Mathematics 2023-07-12 Yuri Trakhinin , Tao Wang

We consider the Cauchy problem to the 3D barotropic compressible Navier-Stokes equation. We prove global well-posedness, assuming that the initial data $(\rho_0-1,u_0)$ has small norms in the critical Besov space…

Analysis of PDEs · Mathematics 2025-09-23 Zihua Guo , Zihao Song , Minghua Yang

We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic solid shell. The fluid motion is governed by the Navier-Stokes equations, while the shell is modeled by…

Analysis of PDEs · Mathematics 2007-05-23 C. H. Arthur Cheng , Daniel Coutand , Steve Shkoller

This paper is concerned with an interaction problem between a full compressible, electrically conducting fluid and a thermoelastic shell in a two-dimensional setting. The shell is modelled by linear thermoelasticity equations, and…

Analysis of PDEs · Mathematics 2025-06-10 Kuntal Bhandari , Bingkang Huang , Šárka Nečasová

We consider the interaction of a viscous incompressible fluid with a flexible shell in three space dimensions. The fluid is described by the three-dimensional incompressible Navier--Stokes equations in a domain that is changing in…

Analysis of PDEs · Mathematics 2023-07-25 Dominic Breit , Prince Romeo Mensah , Sebastian Schwarzacher , Pei Su

We consider a fluid-structure interaction system composed by a three-dimensional viscous incompressible fluid and an elastic plate located on the upper part of the fluid boundary. The fluid motion is governed by the Navier-Stokes system…

Analysis of PDEs · Mathematics 2022-04-12 Imene Aicha Djebour

We are interested in studying a system coupling the compressible Navier-Stokes equations with an elastic structure located at the boundary of the fluid domain. Initially the fluid domain is rectangular and the beam is located on the upper…

Analysis of PDEs · Mathematics 2018-08-22 Sourav Mitra

We address semigroup well-posedness for a linear, compressible viscous fluid interacting at its boundary with an elastic plate. We derive the model by linearizing the compressible Navier-Stokes equations about an arbitrary flow state, so…

Analysis of PDEs · Mathematics 2018-08-17 George Avalos , Pelin Guven Geredeli , Justin T. Webster

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

The large time behavior of the unique strong solution to the barotropic compressible Navier-Stokes system is studied with large external forces and initial data, where the shear viscosity is a positive constant and the bulk one is…

Analysis of PDEs · Mathematics 2023-10-25 Xinyu Fan , Jing Li , Xue Wang

In this paper, we study a nonlinear interaction problem between compressible viscous fluids and plates. For this problem, we introduce relative entropy and relative energy inequality for the finite energy weak solutions (FEWS). First, we…

Analysis of PDEs · Mathematics 2021-12-14 Srđan Trifunović

We address a system of equations modeling a compressible fluid interacting with an elastic body in dimension three. We prove the local existence and uniqueness of a strong solution when the initial velocity belongs to the space…

Analysis of PDEs · Mathematics 2026-01-01 Igor Kukavica , Linfeng Li , Amjad Tuffaha

This paper is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in $\R^3$. For less regular data and weaker compatibility condition than those…

Analysis of PDEs · Mathematics 2021-10-28 Suhua Lai , Hao Xu , Jianwen Zhang

We prove existence of a unique global-in-time weak solutions of the Navier-Stokes equations that govern the motion of a compressible viscous fluid with density-dependent viscosity in two-dimensional space. The initial velocity belongs to…

Analysis of PDEs · Mathematics 2024-09-18 Sagbo Marcel Zodji

For the physically important case in which the viscosity coefficients depend on the density $\rho$ through a power law (i.e., $\rho^\delta$ with some exponent $\delta \in (\frac{1}{2},1)$), we establish the global well-posedness of regular…

Analysis of PDEs · Mathematics 2026-05-19 Gui-Qiang G. Chen , Jiawen Zhang , Shengguo Zhu

In this paper, the one-dimensional compressible Navier-Stokes system with outer pressure boundary conditions is investigated. Under some suitable assumptions, we prove that the specific volume and the temperature are bounded from below and…

Analysis of PDEs · Mathematics 2022-06-01 Guocai Cai , Canpei Chen , Yanfang Peng

We prove probabilistic well-posedness for a 2D viscous nonlinear wave equation modeling fluid-structure interaction between a 3D incompressible, viscous Stokes flow and nonlinear elastodynamics of a 2D stretched membrane. The focus is on…

Analysis of PDEs · Mathematics 2022-06-07 Jeffrey Kuan , Tadahiro Oh , Sunčica Čanić

We prove the local well-posedness for the barotropic compressible Navier-Stokes system on a moving domain, a motion of which is determined by a given vector field ${\bf V}$, in a maximal $L_p-L_q$ regularity framework. Under additional…

Analysis of PDEs · Mathematics 2020-11-03 Ondrej Kreml , Sárka Necasová , Tomasz Piasecki

We study the existence of weak martingale solutions to a stochastic moving boundary problem arising from the interaction between an isentropic compressible fluid and a viscoelastic structure. In the model, we consider a three-dimensional…

Analysis of PDEs · Mathematics 2025-05-22 Jeffrey Kuan , Krutika Tawri

We analyze a Navier-Stokes-Cahn-Hilliard model for viscous incompressible two-phase flows where the mechanisms of chemotaxis, active transport and reaction are taken into account. The evolution system couples the Navier-Stokes equations for…

Analysis of PDEs · Mathematics 2024-06-03 Jingning He , Hao Wu