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We consider the two-phase flow model with slip boundary condition in a 3D exterior domains whose boundary is smooth. We establish the global existence of classical solutions of this system provided that the initial energy is suitably small.…

Analysis of PDEs · Mathematics 2022-11-16 Zilai Li , Hao Liu , Huaqiao Wang

This paper is devoted to the well-posedness theory of piston problem for compressible {combustion} Euler flows with physical ignition condition. A significant combustion phenomena called detonation will occur provided the reactant is…

Analysis of PDEs · Mathematics 2022-03-04 Kai Hu , Jie Kuang

In this work we systematically derive the governing equations of supersonic conical flow by projecting the 3D Euler equations onto the unit sphere. These equations result from taking the assumption of conical invariance on the 3D flow…

Analysis of PDEs · Mathematics 2019-10-22 Ian Holloway , Sivaguru S. Sritharan

We establish global existence of solutions to the compressible Euler equations, in the case that a finite volume of ideal gas expands into vacuum. Vacuum states can occur with either smooth or singular sound speed, the latter corresponding…

Analysis of PDEs · Mathematics 2019-04-03 Steve Shkoller , Thomas C. Sideris

In this paper, we obtain a result on the existence and uniqueness of global spherically symmetric classical solutions to the compressible isentropic Navier-Stokes equations with vacuum in a bounded domain or exterior domain {\Omega} of Rn(n…

Analysis of PDEs · Mathematics 2012-05-01 Shijin Ding , Huanyao Wen , Lei Yao , Changjiang Zhu

We establish the existence of a stable family of solutions to the Euler equations on Kasner backgrounds near the singularity with the full expected asymptotic data degrees of freedom and no symmetry or isotropy restrictions. Existence is…

Analysis of PDEs · Mathematics 2025-02-17 Florian Beyer , Todd A. Oliynyk

We formulated a problem on hypersonic limit of two-dimensional steady non-isentropic compressible Euler flows passing a straight wedge. It turns out that Mach number of the upcoming uniform supersonic flow increases to infinite may be taken…

Analysis of PDEs · Mathematics 2019-04-09 Aifang Qu , Hairong Yuan , Qin Zhao

We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate…

Analysis of PDEs · Mathematics 2013-11-07 Gui-Qiang Chen , Changguo Xiao , Yongqian Zhang

We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form with a combination of acoustic and Dirichlet boundary…

General Relativity and Quantum Cosmology · Physics 2019-07-23 Todd A. Oliynyk

We are concerned with inverse problems for supersonic potential flows past infinite axisymmetric Lipschitz cones. The supersonic flows under consideration are governed by the steady isentropic Euler equations for axisymmetric potential…

Analysis of PDEs · Mathematics 2023-10-30 Gui-Qiang G. Chen , Yun Pu , Yongqian Zhang

We establish the global well-posedness of classical solutions to the vacuum free boundary problem of the 1-D viscous Saint-Venant system with large data. Since the depth $\rho$ of the fluid vanishes on the moving boundary, the momentum…

Analysis of PDEs · Mathematics 2025-04-15 Xin Zhouping , Zhang Jiawen , Zhu Shengguo

We prove global existence and asymptotic behavior of classical solutions for two dimensional inviscid Rotating Shallow Water system with small initial data subject to the zero-relative-vorticity constraint. One of the key steps is a…

Analysis of PDEs · Mathematics 2009-07-01 Bin Cheng , Chunjing Xie

In this paper, we study the stability of supersonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle of varying cross-sections. We formulate the problem as an initial-boundary value…

Analysis of PDEs · Mathematics 2018-04-16 Feimin Huang , Jie Kuang , Dehua Wang , Wei Xiang

The motion of a compressible inviscid radiative flow can be described by the radiative Euler equations, which consists of the Euler system coupled with a Poisson equation for the radiative heat flux through the energy equation. Although…

Analysis of PDEs · Mathematics 2024-09-24 Huijiang Zhao , Boran Zhu

We are concerned with the low regularity of self-similar solutions of two-dimensional Riemann problems for the isentropic Euler system. We establish a general framework for the analysis of the local regularity of such solutions for a class…

Analysis of PDEs · Mathematics 2026-02-27 Gui-Qiang G. Chen , Mikhail Feldman , Wei Xiang

We study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a…

Analysis of PDEs · Mathematics 2024-08-22 Yang Liu , Xin Zhong

This work is devoted to study the global existence of strong and classical solutions to compressible Navier-Stokes equations with or without density jump on the moving boundary for spherically symmetric motion. We establish a unified method…

Analysis of PDEs · Mathematics 2020-07-07 Xin Liu

The full compressible magnetohydrodynamic system in three-dimensional exterior domains is investigated. For the initial-boundary-value problem of this system with slip boundary condition for the velocity, adiabatic one for the temperature,…

Analysis of PDEs · Mathematics 2022-11-02 Yunkun Chen , Yi Peng , Xue Wang

We consider the local well-posedness of the one-dimensional nonisentropic Euler equations with moving physical vacuum boundary condition. The physical vacuum singularity requires the sound speed to be scaled as the square root of the…

Analysis of PDEs · Mathematics 2019-05-29 Yongcai Geng , Yachun Li , Dehua Wang , Runzhang Xu

This paper is concerned with the global existence and uniqueness of classical solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients in three-dimensional bounded domains or in the whole space…

Analysis of PDEs · Mathematics 2026-05-01 Qinghao Lei