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In this paper, we prove the global existence of strong solutions to the two-dimensional compressible MHD equations with density dependent viscosity coefficients (known as Kazhikhov-Vaigant model) on 2D solid balls with arbitrary large…

Analysis of PDEs · Mathematics 2023-10-18 Xiangdi Huang , Wei Yan

In this paper, we mainly consider the global solvability of smooth solutions for the Cauchy problem of the three-dimensional Landau-Lifshitz-Slonczewski equation in the Morrey space. We derive the covariant complex Ginzburg-Landau equation…

Analysis of PDEs · Mathematics 2023-07-13 Chenlu Zhang , Huaqiao Wang

This paper considers the Cauchy problem of equations for the viscous compressible and heat-conductive fluids in the two-dimensional(2D) space. We establish the local existence theory of unique strong solution under some initial layer…

Analysis of PDEs · Mathematics 2019-07-25 Zhilei Liang

We prove the global-in-time existence of large-data finite-energy weak solutions to an incompressible hybrid Vlasov-magnetohydrodynamic model in three space dimensions. The model couples three essential ingredients of magnetized plasmas: a…

Analysis of PDEs · Mathematics 2017-07-05 Bin Cheng , Endre Süli , Cesare Tronci

We study the global existence of classical solutions for two-dimensional incompressible MHD system with only magnetic diffusion. By using the time-weighted lower-order energy and uniformly bounded higher-order energy estimates, we prove the…

Analysis of PDEs · Mathematics 2023-10-27 Yuanyuan Qiao

An initial boundary value problem for compressible Magnetohydrodynamics (MHD) is considered on an exterior domain (with the first Betti number vanishes) in $R^3$ in this paper. The global existence of smooth solutions near a given constant…

Analysis of PDEs · Mathematics 2022-11-23 Hairong Liu , Tao Luo , Hua Zhong

In this paper, we address the existence of global solutions to the Cauchy problem for the integrable nonlocal modified Korteweg-de vries (nonlocal mKdV) equation with the initial data $u_0 \in H^{3}(\mathbb{R}) \cap H^{1,1}(\mathbb{R}) $…

Analysis of PDEs · Mathematics 2023-05-29 Anran Liu , Engui Fan

In this paper, we are concerned with the two-dimensional (2D) incompressible magnetohydrodynamic (MHD) equations with velocity dissipation given by $(-\Delta)^{\alpha}$ and magnetic diffusion given by reducing about logarithmic diffusion…

Analysis of PDEs · Mathematics 2023-03-31 Chao Deng , Zhuan Ye , Baoquan Yuan , Jiefeng Zhao

We prove the existence of a mild solution to the three dimensional incompressible stochastic magnetohydrodynamic equations in the whole space with the initial data which belong to the Sobolev spaces.

Analysis of PDEs · Mathematics 2020-07-28 Ildoo Kim , Minsuk Yang

In this paper we are concerned with the global well-posedness for the compressible MHD equations with large data. We show that if the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\lambda$ is the power function of the…

Analysis of PDEs · Mathematics 2012-04-26 Dongfen Bian , Boling Guo

Compressible vortex sheets are fundamental waves in entropy solutions to the multidimensional hyperbolic systems of conservation laws. For the Euler equations in 2-D gas dynamics, the classical linearized stability analysis on compressible…

Analysis of PDEs · Mathematics 2007-05-23 Gui-Qiang Chen , Ya-Guang Wang

We study the singularity formation of strong solutions to the two-dimensional (2D) Cauchy problem of the non-baratropic compressible magnetohydrodynamic equations without heat conductivity. It is proved that the strong solution exists…

Analysis of PDEs · Mathematics 2018-09-05 Xin Zhong

We study the incompressible limit of the compressible non-isentropic magnetohydrodynamic equations with zero magnetic diffusivity and general initial data in the whole space $\mathbb{R}^d$ $(d=2,3)$. We first establish the existence of…

Analysis of PDEs · Mathematics 2011-11-15 Song Jiang , Qiangchang Ju , Fucai Li

This paper is concerned with the three-dimensional equations of a simplified hydrodynamic flow modeling the motion of compressible, nematic liquid crystal materials. The authors establish the global existence of classical solution to the…

Analysis of PDEs · Mathematics 2012-04-24 Jing Li , Zhonghai Xu , Jianwen Zhang

In this paper, we consider the Cauchy problem for the three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering the system as an elliptic-dominated structure and defining suitable…

Analysis of PDEs · Mathematics 2024-08-09 Xiangdi Huang , Jiaxu Li , Rong Zhang

We start with the classic result that the Cauchy problem for ideal compressible gas dynamics is locally well posed in time in the sense of Hadamard; there is a unique solution that depends continuously on initial data in Sobolev space $H^s$…

Analysis of PDEs · Mathematics 2016-11-18 Barbara Lee Keyfitz , Feride Tiglay

This paper solves the global well-posedness and stability problem on a special $2\frac12$-D compressible viscous non-resistive MHD system near a steady-state solution. The steady-state here consists of a positive constant density and a…

Analysis of PDEs · Mathematics 2022-11-11 Boqing Dong , Jiahong Wu , Xiaoping Zhai

This paper investigates an initial-boundary value problem for three-dimensional (3D) micropolar fluids in a strip domain, including both the compressible and the (homogeneous and inhomogeneous) incompressible cases in the absence of angular…

Analysis of PDEs · Mathematics 2026-05-21 Youyi Zhao

Due to the absence of dissipation mechanism to the inviscid compressible systems, it is a challenging problem to prove their global solvability. In this paper, we are concerned with the initial-boundary value problem to the inviscid and…

Analysis of PDEs · Mathematics 2025-08-20 Jinkai Li , Liening Qiao

As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole space is proved in some suitable weighted Sobolev spaces…

Analysis of PDEs · Mathematics 2010-10-28 Radjesvarane Alexandre , Y. Morimoto , Seiji Ukai , Chao-Jiang Xu , Tong Yang