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A main result of this paper establishes the global stability of the 3D MHD equations with mixed partial dissipation near a background magnetic field in the domain $\Omega=\mathbb{T}^2\times\mathbb{R}$ with $\mathbb{T}^2=[0, 1]^2$. More…

Analysis of PDEs · Mathematics 2024-02-05 Xuemin Deng , Yuelong Xiao , Aibin Zang

In this paper, we prove the existence of global weak solutions to the compressible two-fluid Navier-Stokes equations in three dimensional space. The pressure depends on two different variables from the continuity equations. We develop an…

Analysis of PDEs · Mathematics 2017-10-17 Alexis Vasseur , Huanyao Wen , Cheng Yu

This paper is concerned with a compressible MHD equations describing the evolution of viscous non-resistive fluids in piecewise regular bounded Lipschitz domains. Under the general inflow-outflow boundary conditions, we prove existence of…

Analysis of PDEs · Mathematics 2025-01-28 Yang Li , Young-Sam Kwon , Yongzhong Sun

This paper is concerned with the stability and large-time behavior for 3D magneto-micropolar equations with horizontal dissipation. The global well-posedness of the aforementioned system is established, with the initial data and its…

Analysis of PDEs · Mathematics 2025-09-25 Peng Lu , Yuanyuan Qiao

In this article we study the asymptotic behavior of a quadratic NLS equation with small, time-dependent potential and small spatially localized initial data. We prove global existence and scattering of solutions. The two main ingredients of…

Analysis of PDEs · Mathematics 2021-12-22 Tristan Léger

We consider the problem of small data global existence for a class of semilinear wave equations with null condition on a Lorentzian background $(\mathbb{R}^{3+1}, g)$ with a \textbf{time dependent metric $g$} coinciding with Minkowski…

Analysis of PDEs · Mathematics 2012-04-30 Shiwu Yang

Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution…

Analysis of PDEs · Mathematics 2017-06-06 Andrei V. Faminskii

This paper investigates the global existence and the decay rate in time of a solution to the Cauchy problem for an incompressible Oldroyd model with a deformation tensor damping term. There are three major results. The first is the global…

Analysis of PDEs · Mathematics 2017-05-15 Baoquan Yuan , Yun Liu

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 investigates the existence and uniqueness of local strong solutions to the three-dimensional compressible magnetohydrodynamic (MHD) equations with density-dependent viscosities in an exterior domain. The system models the…

Analysis of PDEs · Mathematics 2025-04-08 Hairong Liu , Tao Luo , Hua Zhong

This paper resolves the global regularity problem for the three-dimensional compressible magnetohydrodynamics (MHD) equations in the three-dimensional whole space, in the presence of a background magnetic field. Motivated by geophysical…

Analysis of PDEs · Mathematics 2026-05-13 Jincheng Gao , Xianpeng Hu , Lianyun Peng , Jiahong Wu

The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…

Classical Analysis and ODEs · Mathematics 2025-01-09 Alberto Lastra

We examine the so-called micropolar equations in three dimensional cylindrical domains under Navier boundary conditions. These equations form a generalization of the ordinary incompressible Navier-Stokes model, taking the structure of the…

Analysis of PDEs · Mathematics 2013-02-20 B. Nowakowski

In this article, we prove that small localized data yield solutions to Kawahara type equation which have linear dispersive decay on a finite time. We use the similar method used to derive the dispersive decay bound of the solutions to the…

Analysis of PDEs · Mathematics 2022-11-29 Jongwon Lee

This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak…

Analysis of PDEs · Mathematics 2017-02-28 Dongfen Bian , Jitao Liu

This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this…

Analysis of PDEs · Mathematics 2011-11-29 Le Xuan Truong , Le Thi Phuong Ngoc , Alain Pham Ngoc Dinh , Nguyen Thanh Long

We formulate on rectangles and on the right horizontal half-strip initial-boundary value problems for a two-dimensional Benney-Lin type equation. Existence and uniqueness of a regular solution as well as the exponential decay rate for the…

Analysis of PDEs · Mathematics 2023-07-18 Nikolai Larkin

We study an anisotropic system arising in magnetohydrodynamics (MHD) in the whole space R^3 , in the case where there are no diffusivity in the vertical direction and only a small diffusivity in the horizontal direction (of size…

Analysis of PDEs · Mathematics 2017-08-15 Van-Sang Ngo

In this paper, we prove the global existence of analytical solutions to the compressible Oldroyd-B model without retardation near a non-vacuum equilibrium in ${\mathbb R}^n$ $(n=2,3)$. Zero retardation results in zero dissipation in the…

Analysis of PDEs · Mathematics 2023-06-01 Xinghong Pan

This paper aims to establish the global well-posedness of the free boundary problem for the incompressible viscous resistive magnetohydrodynamic (MHD) equations. Under the framework of Lagrangian coordinates, a unique global solution exists…

Analysis of PDEs · Mathematics 2024-08-29 Wei Zhang , Jie Fu , Chengchun Hao , Siqi Yang