首页/论文/2011.04043

arXiv 2011.040432020-11-08math.APmath-phmath.MP

Hydrostatic approximation of the 2D MHD system in a thin strip with a small analytic data

Nacer Aarach

DOI：: 10.1016/j.jmaa.2021.125949

英文摘要：

In this paper, we study the global well-posedness of the two dimensional rescaled anisotropic MHD system and also to the hydrostatic MHD with no slip boundary condition in a strip, for small initial data, which are analytic in the horizontal variable. We also justify the limit of the MHD system (when $ε\to 0$ where $ε$ denotes the height of the initial strip) is given by a couple of a Prandtl like system for the velocity and a magnetic field equation when the initial data are small and analytic.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

磁流体静力学MHD波系统的Gevrey适定性

Gevrey well-posedness of the hydrostatic MHD-wave system

本文研究了磁流体静力学MHD波系统的适定性，采用边界分解方法，在Gevrey 7/6空间中证明了凸初始数据的局部适定性。

2025-12-06math.AP

On the hydrostatic approximation of the Navier-Stokes equations in a thin strip

In this paper, we first prove the global well-posedness of a scaled anisotropic Navier-Stokes system and the hydrostatic Navier-Stokes system in a 2-D striped domain with small analytic data in the tangential variable. Then we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes system with analytic data.

2019-04-09math.AP

3D hyperbolic Navier-Stokes equations in a thin strip: global well-posedness and hydrostatic limit in Gevrey space

We consider the hyperbolic version of three-dimensional anisotropic Naver-Stokes equations in a thin strip and its hydrostatic limit that is a hyperbolic Prandtl type equations. We prove the global-in-time existence and uniqueness for the two systems and the hydrostatic limit when the initial data belong to the Gevrey function space with index 2. The proof is based on a direct energy method by observing the damping effect in the systems.

2022-04-20math.AP

Hydrostatic approximation of the 2D primitive equations in a thin strip

We prove the global wellposedness of the 2D non-rotating primitive equations with no-slip boundary conditions in a thin strip of width $\eps$ for small data which are analytic in the tangential direction. We also prove that the hydrostatic limit (when $\eps \to 0$) is a couple of a Prandtl-like system for the velocity with a transport-diffusion equation for the temperature.

2023-02-26math.AP

薄条区域中 Beris-Edwards 系统的流体静力学极限

On hydrostatic limit of Beris-Edwards system in a thin strip

研究薄条中3D共旋Beris-Edwards系统的流体静力学极限，证明在特定尺度下系统收敛于流体部分为Prandtl系统、$Q$-张量部分为非标准系统的解耦极限，并建立Sobolev空间中的适定性。

2024-11-14math.AP

Global well-posedness of 2D Hyperbolic perturbation of the Navier-Stokes system in a thin strip

In this paper, we study a hyperbolic version of the Navier-Stokes equations, obtained by using the approximation by relaxation of the Euler system, evolving in a thin strip domain. The formal limit of these equations is a hyperbolic Prandtl type equation, our goal is to prove the existence and uniqueness of a global solution to these equations for analytic initial data in the tangential variable, under a uniform smallness assumption. Then we justify the limit from the anisotropic hyperbolic Navier-Stokes system to the hydrostatic hyperbolic Navier-Stokes system with small analytic data.

2023-01-18math-phmath.APmath.MP

更多相关论文收起更多论文

Hydrostatic limit of the Navier-Stokes-alpha model

In this paper we study the hydrostatic limit of the Navier-Stokes-alpha model in a very thin striped domain. We derive some Prandtl-type limit equations for this model and we prove the global well-posedness of the limit system for small initial conditions in an appropriate analytic function space.

2021-10-04math.AP

二维情形下Beris-Edwards系统的流体静力学极限

The hydrostatic limit of the Beris-Edwards system in dimension two

该研究针对二维共转Beris-Edwards液晶系统，证明薄带域小解析初值下的全局适定性，并验证其向含流体静力学Navier-Stokes系统的极限收敛性。

2023-05-03math.AP

Global regularity for the 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion

This paper establishes the global regularity of classical solution to the 2D MHD system with only horizontal dissipation and horizontal magnetic diffusion in a strip domain $\mathbb{T}\times\mathbb{R}$ when the initial data is suitable small. To prove this, we combine the Littlewood-Paley decomposition with anisotropic inequalities to establish a crucial commutator estimate. We also analysis the asymptotic behavior of the solution. In addition, the global existence and uniqueness of classical solution is obtained for the 2D simplified tropical climate model with only horizontal dissipations.

2020-09-28math.AP

Global hydrostatic approximation of hyperbolic Navier-Stokes system with small Gevrey class data

We investigate the hydrostatic approximation of a hyperbolic version of Navier-Stokes equations, which is obtained by using Cattaneo type law instead of Fourier law, evolving in a thin strip $\R\times (0,\varepsilon)$. The formal limit of these equations is a hyperbolic Prandtl type equation. We first prove the global existence of solutions to these equations under a uniform smallness assumption on the data in Gevrey $2$ class. Then we justify the limit globally-in-time from the anisotropic hyperbolic Navier-Stokes system to the hyperbolic Prandtl system with such Gevrey $2$ class data. Compar…

2021-11-24math.APmath.AT

剪切磁场下二维不可压缩粘性无电阻磁流体动力学的全局非线性稳定性

Global nonlinear stability of the 2D incompressible viscous non-resistive MHD under sheared magnetic field

Fudan University（复旦大学）；Donghua University（东华大学）；Shanghai University of Finance and Economics（上海财经大学）

研究周期带状区域中二维不可压缩粘性无电阻磁流体动力学在光滑剪切背景磁场下的全局适定性和非线性稳定性，通过拉格朗日坐标和体积保持校正子将线性压力转化为二次非线性，获得全局能量界和各向异性代数衰减率。

2026-08-05math.AP

关于具有二维电场的Navier-Stokes-Maxwell系统的流体静力学近似

On The Hydrostatic Approximation of Navier-Stokes-Maxwell System with 2D Electronic Fields

本文研究二维条状区域中尺度化各向异性Navier-Stokes-Maxwell系统的流体静力学近似，证明局部与全局适定性、指数衰减，并验证Gevrey-2正则性的最优性。

2024-11-10math.AP

On the ideal magnetohydrodynamics in three-dimensional thin domains: well-posedness and asymptotics

We consider the ideal magnetohydrodynamics (MHD) subjected to a strong magnetic field along $x_1$ direction in three-dimensional thin domains $Ω_δ=\mathbb{R}^2\times(-δ,δ)$ with slip boundary conditions. It is well-known that in this situation the system will generate Alfvén waves. Our results are summarized as follows: (i).\, We construct the global solutions (Alfvén waves) to MHD in the thin domain $Ω_δ$ with $δ>0$. In addition, the uniform energy estimates are obtained with respected to the parameter $δ$. (ii). We justify the asymptotics of the MHD equations from the thin domain $Ω_δ$ to th…

2018-03-30math.AP