scholarly journals On the Global Solution of a 3-D MHD System with Initial Data near Equilibrium

2016 ◽  
Vol 70 (8) ◽  
pp. 1509-1561 ◽  
Author(s):  
Hammadi Abidi ◽  
Ping Zhang
Keyword(s):  
Initial Data ◽  
Global Solution ◽  
Mhd System

scholarly journals Global solution to the 3-D inhomogeneous incompressible MHD system with discontinuous density

2019 ◽  
Vol 12 (1) ◽  
pp. 37-58 ◽  
Author(s):  
Fei Chen ◽  
◽  
Boling Guo ◽  
Xiaoping Zhai ◽  
◽  
...  
Keyword(s):  
Global Solution ◽  
Mhd System ◽  
Incompressible Mhd

scholarly journals GLOBAL SOLUTION FOR THE GENERALIZED ANISOTROPIC NAVIER–STOKES EQUATIONS WITH LARGE DATA

2015 ◽  
Vol 20 (2) ◽  
pp. 205-231 ◽  
Author(s):  
Daoyuan Fang ◽  
Bin Han
Keyword(s):  
Initial Data ◽  
Besov Space ◽  
Global Solution ◽  
Stokes Equations ◽  
Large Data ◽  
Navier Stokes ◽  
Unique Global Solution ◽  
Large Initial Data ◽  
Navier Stokes Equations ◽  
Anisotropic Besov Space

We are concerned with 3D incompressible generalized anisotropic Navier– Stokes equations with hyperdissipative term in horizontal variables. We prove that there exists a unique global solution for it with large initial data in anisotropic Besov space.

scholarly journals Global well-posedness for the three-dimensional incompressible viscous non-resistive MHD equations in an infinite slab

2021 ◽  
Author(s):  
Youyi Zhao
Keyword(s):  
Initial Data ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Well Posedness ◽  
Lagrangian Coordinates ◽  
Mathematical Approach ◽  
Compatibility Conditions ◽  
Finite Height ◽  
Infinite Slab ◽  
Mhd System

In this paper, we investigate the global well-posedness of the system of incompressible viscous non-resistive MHD fluids in a three-dimensional horizontally infinite slab with finite height. We reformulate our analysis to Lagrangian coordinates, and then develop a new mathematical approach to establish global well-posedness of the MHD system, which requires no nonlinear compatibility conditions on the initial data.

scholarly journals Constructive Approach of the Solution of Riemann Problem for Shallow Water Equations with Topography and Vegetation

2020 ◽  
Vol 28 (2) ◽  
pp. 93-114
Author(s):  
Stelian Ion ◽  
Stefan-Gicu Cruceanu ◽  
Dorin Marinescu
Keyword(s):  
Initial Data ◽  
Shallow Water ◽  
Global Solution ◽  
Riemann Problem ◽  
Hyperbolic System ◽  
Shallow Water Equations ◽  
Local Existence ◽  
Water Model ◽  
Constructive Approach ◽  
Shallow Water Model

AbstractWe investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not supposed to be “small enough”). One di culty for the extended solution arises from the double degeneracy of the hyperbolic system describing the model. Another di culty is given by the fact that the construction of the solution assumes solving an equation which has no global solution. Finally, we present some cases to illustrate the existence and non-existence of the solution.

scholarly journals Vanishing shear viscosity limit and boundary layer study for the planar MHD system

2019 ◽  
Vol 29 (06) ◽  
pp. 1139-1174 ◽  
Author(s):  
Xulong Qin ◽  
Tong Yang ◽  
Zheng-an Yao ◽  
Wenshu Zhou
Keyword(s):  
Boundary Layer ◽  
Initial Data ◽  
Global Existence ◽  
Shear Viscosity ◽  
Initial Boundary ◽  
Heat Conductivity Coefficient ◽  
Large Initial Data ◽  
Initial Boundary Problem ◽  
Viscosity Limit ◽  
Mhd System

We consider an initial boundary problem for the planar MHD system under the general condition on the heat conductivity coefficient that depends on both the temperature and the density. Firstly, the global existence of strong solution for large initial data is obtained, and then the limit of the vanishing shear viscosity is justified. In addition, the [Formula: see text] convergence rate is obtained together with the estimation on the thickness of the boundary layer.

scholarly journals Global Analysis for Rough Solutions to the Davey-Stewartson System

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Han Yang ◽  
Xiaoming Fan ◽  
Shihui Zhu
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Nonlinear Equation ◽  
Global Solution ◽  
Global Analysis ◽  
Space Time ◽  
Well Posedness ◽  
The Cauchy Problem ◽  
New Space ◽  
Time Bounds

The global well-posedness of rough solutions to the Cauchy problem for the Davey-Stewartson system is obtained. It reads that if the initial data is inHswiths> 2/5, then there exists a global solution in time, and theHsnorm of the solution obeys polynomial-in-time bounds. The new ingredient in this paper is an interaction Morawetz estimate, which generates a new space-timeLt,x4estimate for nonlinear equation with the relatively general defocusing power nonlinearity.

An iteration method for a nonlinear differential equation describing the convergence to equilibrium in a system of reacting polymers

1981 ◽  
Vol 375 (1763) ◽  
pp. 529-542
Keyword(s):  
Differential Equation ◽  
Initial Data ◽  
Global Solution ◽  
Nonlinear Differential Equation ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Constructive Method ◽  
Convergence To Equilibrium ◽  
Initial Value

A constructive method is presented to give the global solution to a nonlinear initial value problem describing the convergence to equilibrium in a system of reacting polymers. The solution is proved to be unique and continuous with respect to small variations in the initial data.

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