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We establish here the local-in-time well-posedness of strong solutions with large initial data to a system coupling compressible atmospheric dynamics with a refined moisture model introduced in Hittmeir and Klein (Theor. Comput. Fluid Dyn.…

Analysis of PDEs · Mathematics 2024-08-29 Sabine Doppler , Rupert Klein , Xin Liu , Edriss Titi

We study the system of equations which describes barotropic (isentropic) flows of viscous compressible multi-fluids (mixtures of fluids). We study the relations between pressure, densities, concentrations, viscosities and other parameters…

Analysis of PDEs · Mathematics 2017-11-22 Alexander Mamontov , Dmitriy Prokudin

The present paper considers a homogeneous bubble inside an unbounded polytropic compressible liquid with viscosity. The system is governed by the Navier-Stokes equation with free boundary which is determined by the kinematic and dynamic…

Analysis of PDEs · Mathematics 2022-12-02 Lifeng Zhao , Liangchen Zou

We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…

Analysis of PDEs · Mathematics 2025-02-18 Noah Stevenson , Ian Tice

We investigate a Hele-Shaw type free boundary problem in one spatial dimension, where heterogeneities appear both on the free boundary and within the interior of the positivity set. Our contributions are twofold. First, we establish…

Analysis of PDEs · Mathematics 2025-08-20 Olga Turanova , Yuming Paul Zhang

We first show local-in-time well-posedness of the compressible Navier-Stokes equations, assuming striated regularity while no other smoothness or smallness conditions on the initial density. With these local-in-time solutions served as…

Analysis of PDEs · Mathematics 2024-05-21 Xian Liao , Sagbo Marcel Zodji

We consider the plasma-vacuum interface problem in a horizontally periodic slab impressed by a uniform non-horizontal magnetic field. The lower plasma region is governed by the incompressible inviscid and resistive MHD, the upper vacuum…

Analysis of PDEs · Mathematics 2021-12-17 Yanjin Wang , Zhouping Xin

In this paper we establish the incompressible limit for the compressible free-boundary Euler equations with surface tension in the case of a liquid. Compared to the case without surface tension treated recently, the presence of surface…

Analysis of PDEs · Mathematics 2020-05-14 Marcelo M. Disconzi , Chenyun Luo

Initial-boundary value problem for linearized equations of motion of viscous barotropic fluid in a bounded domain is considered. Existence, uniqueness and estimates of weak solutions to this problem are derived. Convergence of the solutions…

Analysis of PDEs · Mathematics 2015-05-20 Nikolay Gusev

We study microlocally the transmission problem at the interface between an isotropic linear elastic solid and a linear inviscid fluid. We set up a system of evolution equations describing the particle displacement and velocity in the solid,…

Analysis of PDEs · Mathematics 2021-11-08 Nikolas Eptaminitakis , Plamen Stefanov

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

The global well-posedness and inviscid limit are investigated for the fluid-particle interaction system, described by the Navier-Stokes equations for the inhomogeneous incompressible viscous flows coupled with the Vlasov-Fokker-Planck…

Analysis of PDEs · Mathematics 2025-12-15 Fucai Li , Jinkai Ni , Ling-Yun Shou , Dehua Wang

We study the local-in-time well-posedness for an interface that separates an anisotropic plasma from a vacuum. The plasma flow is governed by the ideal Chew-Goldberger-Low (CGL) equations, which are the simplest collisionless fluid model…

Analysis of PDEs · Mathematics 2023-07-05 Yuri Trakhinin

We study the motion of a rigid body within a compressible, isentropic, and viscous fluid contained in a fixed bounded domain $\Omega \subset \mathbb{R}^3$. The fluid's behavior is described by the Navier-Stokes equations, while the motion…

Analysis of PDEs · Mathematics 2024-08-15 Šimon Axmann , Šárka Nečasová , Ana Radošević

We consider a viscous compressible barotropic flow in the interval $[0,\pi]$ with homogeneous Dirichlet boundary conditions for the flow velocity and a constant rest state as initial data. Given two sufficiently close subintervals…

Analysis of PDEs · Mathematics 2025-07-11 Kai Koike , Franck Sueur , Gastón Vergara-Hermosilla

We consider an isotropic compressible non-dissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid as well as the free…

Fluid Dynamics · Physics 2020-10-28 Alexander G. Abanov , Tankut Can , Sriram Ganeshan , Gustavo M. Monteiro

We investigate the initial value problem of a very general class of $3+1$ non-Newtonian compressible fluids in which the viscous stress tensor with shear and bulk viscosity relaxes to its Navier-Stokes values. These fluids correspond to the…

Analysis of PDEs · Mathematics 2023-12-04 Ariel Lerman , Marcelo M. Disconzi , Jorge Noronha

The theory of turbulent Newtonian fluids turns out that the choice of the boundary condition is a relevant issue, since it can modify the behavior of the fluid by creating or avoiding a strong boundary layer. In this work we study…

Analysis of PDEs · Mathematics 2017-05-03 Nikolai Chemetov , Fernanda Cipriano

We consider the linearized 2D inviscid shallow water equations in a rectangle. A set of boundary conditions is proposed which make these equations well-posed. Several different cases occur depending on the relative values of the reference…

Analysis of PDEs · Mathematics 2015-06-11 Aimin Huang , Roger Temam

The hard phase model describes a relativistic barotropic irrotational fluid with sound speed equal to the speed of light. In this paper, we prove the local well-posedness for this model in the Minkowski background with free boundary.…

Analysis of PDEs · Mathematics 2020-05-26 Shuang Miao , Sohrab Shahshahani , Sijue Wu