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Extended magnetohydrodynamics (XMHD) is a fluid plasma model generalizing ideal MHD by taking into account the impact of Hall drift effects and the influence of electron inertial effects. XMHD has a Hamiltonian structure which has received…

Analysis of PDEs · Mathematics 2024-06-26 Christophe Cheverry , Nicolas Besse

In this paper we consider the global well-posedness of compressible magnetohydrodynamic system in $\R^d$ with $d\geq2$, in the framework of the critical Besov spaces. We can show that if the initial data, the shear viscosity and the…

Analysis of PDEs · Mathematics 2018-05-01 Jinlu Li , Yanghai Yu , Weipeng Zhu

This paper studies the local existence of strong solutions to the Cauchy problem of the 2D fluid-particle interaction model with vacuum as far field density. Notice that the technique used by Ding et al.\cite{SBH} for the corresponding 3D…

Analysis of PDEs · Mathematics 2016-09-04 Yang Liu

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

We study the Cauchy problem of the incompressible micropolar fluid system in $\mathbb{R}^{3}$. In a recent work of the first author and Jihong Zhao \cite{ZhuZ18}, it is proved that the Cauchy problem of the incompressible micropolar fluid…

Analysis of PDEs · Mathematics 2018-05-09 Weipeng Zhu

We study the hydrodynamic behavior of three dimensional (3D) incompressible collections of self-propelled entities in contact with a momentum sink in a state with non-zero average velocity, hereafter called 3D easy-plane incompressible…

Soft Condensed Matter · Physics 2018-10-31 Leiming Chen , Chiu Fan Lee , John Toner

In this paper, we study the global existence of classical solutions to the three dimensional incompressible viscous magneto-hydrodynamical system without magnetic diffusion on periodic boxes, i.e., with periodic boundary conditions. We work…

Analysis of PDEs · Mathematics 2018-03-06 Ronghua Pan , Yi Zhou , Yi Zhu

In our earlier work \cite{DLL}, we have shown the global well-posedness of strong solutions to the three-dimensional primitive equations with the magnetic field (PEM) on a thin domain. The heart of this paper is to provide a rigorous…

Analysis of PDEs · Mathematics 2022-08-04 Lili Du , Dan Li

In this paper, we consider the Cauchy problem to the three dimensional heat conducting compressible nematic liquid crystal system in the presence of vacuum and with vacuum far fields. Global well-posedness of strong solutions is established…

Analysis of PDEs · Mathematics 2021-12-20 Jinkai Li , Qiang Tao

In this paper, the Cauchy problem for a one-dimensional heat conducting compressible non-Newtonian fluid is considered. The constitute equation of the non-Newtonian fluid is determined by two nonlinear terms $(|u_x|^{q-2}u_x)_x$ and…

Analysis of PDEs · Mathematics 2026-03-03 Li Fang , Yu Wang , Aibin Zang

Whether or not the classical solutions of the two-dimensional (2D) incompressible magnetohydrodynamics (MHD) equations with only Laplacian magnetic diffusion (without velocity dissipation) are globally well-posed is a difficult problem and…

Analysis of PDEs · Mathematics 2023-03-31 Zhuan Ye

This paper is concerned with the Cauchy problem for the modified two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity. By fully using the structure of the system, we can obtain the key…

Analysis of PDEs · Mathematics 2026-02-02 Bing Yuan , Rong Zhang , Peng Zhou

In this article, we prove various illposedness results for the Cauchy problem for the incompressible Hall- and electron-magnetohydrodynamic (MHD) equations without resistivity. These PDEs are fluid descriptions of plasmas, where the effect…

Analysis of PDEs · Mathematics 2021-01-07 In-Jee Jeong , Sung-Jin Oh

In this paper we consider the motion of a rigid body in a viscous incompressible fluid when some Navier slip conditions are prescribed on the body's boundary. The whole system "viscous incompressible fluid + rigid body" is assumed to occupy…

Analysis of PDEs · Mathematics 2024-12-30 Gabriela Planas , Franck Sueur

We investigate the existence and uniqueness issues of the 3D incompressible Hall-magnetohydrodynamic system supplemented with initial velocity $u_0$ and magnetic field $B_0$ in critical regularity spaces.In the case where $u_0,$ $B_0$ and…

Analysis of PDEs · Mathematics 2020-11-20 Raphaël Danchin , Jin Tan

This paper investigates the stabilization effect of a background magnetic vorticity on electrically conducting fluids. By exploring the dissipation nature of the linearized equations, we prove the global existence of smooth solutions to the…

Analysis of PDEs · Mathematics 2023-11-16 Yuanyuan Qiao , Yi Zhou

I consider the problem of weakly nonlinear stability of three-dimensional parity-invariant magnetohydrodynamic systems to perturbations, involving large scales. I assume that the MHD state, the stability of which I investigate, does not…

Chaotic Dynamics · Physics 2007-05-23 V. Zheligovsky

In this paper, we investigate the Cauchy problem for the compressible nematic liquid crystal flows in three-dimensional whole space. First of all, we establish the time decay rates for compressible nematic liquid crystal flows by the method…

Analysis of PDEs · Mathematics 2015-03-11 Jincheng Gao , Qiang Tao , Zheng-an Yao

This paper studies the global existence of classical solutions to the two-dimensional incompressible magneto-hydrodynamical (MHD) system with only magnetic diffusion on the periodic domain. The approach is based on a time-weighted energy…

Analysis of PDEs · Mathematics 2018-08-29 Yi Zhou , Yi Zhu

This paper studies the Cauchy problem for a helical vortex filament evolving by the 3D incompressible Navier-Stokes equations. We prove global-in-time well-posedness and smoothing of solutions with initial vorticity concentrated on a helix.…

Analysis of PDEs · Mathematics 2024-02-19 Francisco Gancedo , Antonio Hidalgo-Torné