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Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the…

Analysis of PDEs · Mathematics 2025-07-10 Jiahong Wu , Fuyi Xu , Xiaoping Zhai

The magnetohydrodynamics (MHD) equations are generally known to be difficult to solve numerically, due to their highly nonlinear structure and the strong coupling between the electromagnetic and hydrodynamic variables, especially for high…

Numerical Analysis · Mathematics 2022-11-11 Fabian Laakmann , Patrick E. Farrell , Lawrence Mitchell

The \emph{two-dimensional} (2D) existence result of global(-in-time) solutions for the motion equations of incompressible, inviscid, non-resistive magnetohydrodynamic (MHD) fluids with velocity damping had been established in [Wu--Wu--Xu,…

Analysis of PDEs · Mathematics 2021-05-14 Fei Jiang , Song Jiang , Youyi Zhao

The evolution of electromagnetic and thermodynamic fields in a non-ideal fluid are studied in the framework of ultrarelativistic transverse magnetohydrodynamics (MHD), which is essentially characterized by electric and magnetic fields being…

Nuclear Theory · Physics 2017-12-20 M. Shokri , N. Sadooghi

This paper is denoted to the study of dynamical behavior near explicit finite time blowup solutions for three dimensional incompressible Magnetohydrodynamics (MHD) equations. More precisely, we find a family of explicit finite time blowup…

Analysis of PDEs · Mathematics 2019-07-02 Weiping Yan

This paper concerns the Cauchy problem of the non-baratropic non-resistive magnetohydrodynamic (MHD) equations with zero heat conduction on the whole two-dimensional (2D) space with vacuum as far field density. By delicate weighted energy…

Analysis of PDEs · Mathematics 2018-01-24 Xin Zhong

At the zero temperature limit, a one-dimensional steady solution to the hydrodynamic equation of a U(2) invariant superfluid is obtained. This solution reveals that the magnitude of magnetization is always directly proportional to the…

Quantum Gases · Physics 2025-04-03 Guang-Xin Pang , Yi-Cai Zhang

In this paper, we study the well-posedness of boundary layer problems for the inhomogeneous incompressible magnetohydrodynamics(MHD) equations, which are derived from the two dimensional density-dependent incompressible MHD equations.Under…

Analysis of PDEs · Mathematics 2018-12-18 Jincheng Gao , Daiwen Huang , Zheng-an Yao

We study the Cauchy problem of three-dimensional compressible non-isentropic magnetohydrodynamic (MHD) fluids with both interior and far field vacuum states. Applying delicate energy estimates, initial layer analysis, and continuation…

Analysis of PDEs · Mathematics 2024-08-23 Yang Liu , Xin Zhong

The magnetohydrodynamics (MHD) equations are generally known to be difficult to solve numerically, due to their highly nonlinear structure and the strong coupling between the electromagnetic and hydrodynamic variables, especially for high…

Numerical Analysis · Mathematics 2022-11-22 Fabian Laakmann

The purpose of this article is twofold: first, we introduce a new class of global strong solutions to the magnetohydrodynamic system in $\mathbb{R}^3$ with initial data $(u_0,b_0)$ of arbitrarily large size in any critical space. To do so,…

Analysis of PDEs · Mathematics 2026-04-30 Renato Lucà , Claudia Peña

We prove the global-in-time existence of H^2 solutions of the equations of compressible magnetohydrodynamics with zero magnetic resistivity in three space dimensions. Initial data are taken to be small in H^2 modulo a constant state and…

Analysis of PDEs · Mathematics 2020-11-16 Anthony Suen

In this paper, we are concerned with the initial boundary values problem associated to the compressible viscous non-resistive and heat-conducting magnetohydrodynamic flow, where the magnetic field is vertical. More precisely, by exploiting…

Analysis of PDEs · Mathematics 2024-08-15 Xiaoping Zhai , Yongsheng Li , Yajuan Zhao

In this work we investigate the existence and uniqueness of Struwe-like solutions for a system of partial differential equations modeling the dynamics of magnetoviscoelastic fluids. The considered system couples a Navier-Stokes type…

Analysis of PDEs · Mathematics 2021-03-03 Francesco De Anna , Joshua Kortum , Anja Schlömerkemper

The coupled motion between the hydrodynamic flow and magnetic field introduces significant complexity into the structure of the magnetohydrodynamic (MHD) equations. A key factor contributing to this complexity is the presence of Alfv\'en…

Analysis of PDEs · Mathematics 2025-10-15 Shangkun Weng , Wengang Yang

In this article, we consider a magnetohydrodynamics system for incompressible flow in a three-dimensional bounded domain. Firstly, we give the stability results for our inverse coefficients problem. Secondly, we establish and prove two…

Analysis of PDEs · Mathematics 2018-06-21 Xinchi Huang

In this paper, we investigate the solvability, regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magneto-hydrodynamic (MHD) equations in bounded domains. On the boundary, the velocity field…

Analysis of PDEs · Mathematics 2020-07-07 Qin Duan , Yuelong Xiao , Zhouping Xin

In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit,…

Computational Physics · Physics 2016-06-22 Dinshaw S. Balsara , Takanobu Amano , Sudip Garain , Jinho Kim

This paper is devoted to proving the existence of time-periodic solutions of one-phase or two-phase problems for the Navier-Stokes equations with small periodic external forces when the reference domain is close to a ball. Since our…

Analysis of PDEs · Mathematics 2019-10-01 Thomas Eiter , Mads Kyed , Yoshihiro Shibata

This paper concerns the Cauchy problem of the nonhomogeneous incompressible magnetohydrodynamic (MHD) equations on the whole two-dimensional (2D) space with vacuum as far field density. In particular, the initial density can have compact…

Analysis of PDEs · Mathematics 2015-06-17 Boqiang Lv , Zhonghai Xu , Xin Zhong