scholarly journals Singular Limit of the Rotational Compressible Magnetohydrodynamic Flows

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Young-Sam Kwon
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Relative Entropy ◽  
Convergence Rates ◽  
Singular Limit ◽  
Stratified Flows ◽  
Magnetohydrodynamic Flows ◽  
Mathematical Problems

We consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the stratified flows of the rotational compressible magnetohydrodynamic flows with the well-prepared initial data and the tool of proof is based on the relative entropy. Furthermore, the convergence rates are obtained.

The sharp time decay rates and stability of large solutions to the two-dimensional Phan-Thien–Tanner system with magnetic field

2021 ◽  
pp. 1-34
Author(s):  
Yuhui Chen ◽  
Minling Li ◽  
Qinghe Yao ◽  
Zheng-an Yao
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Convergence Rates ◽  
Splitting Method ◽  
Mhd Flow ◽  
Decay Rates ◽  
Upper And Lower Bounds ◽  
Time Decay ◽  
Large Solutions ◽  
Time Decay Rates

In this paper, we consider the magnetohydrodynamic (MHD) flow of an incompressible Phan-Thien–Tanner (PTT) fluid in two space dimensions. We focus upon the sharp time decay rates (upper and lower bounds) and global-in-time stability of large strong solutions for the PTT system with magnetic field. Firstly, the convergence of large solutions to the equilibrium have been investigated and these convergence rates are shown to be sharp. We then show that two large solutions converge globally in time as long as two initial data are close to each other. One of the main objectives of this paper is to develop a way to capture L 2 -convergence result via auxiliary logarithmic time decay estimates with the initial data in L p ( R 2 ) ∩ L 2 ( R 2 ). Improving time decay rates for the high-order derivatives of large solutions by using interpolation inequalities. In addition, time-weighted energy estimate, Fourier time-splitting method, semigroup method and iterative scheme have also been utilized.

scholarly journals On the differential system govering flows in magnetic field with data inLp

1998 ◽  
Vol 21 (2) ◽  
pp. 299-305 ◽  
Author(s):  
Fengxin Chen ◽  
Ping Wang ◽  
Chaoshun Qu
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Boundary Conditions ◽  
Differential System ◽  
Existence And Uniqueness ◽  
Mhd Equations ◽  
The Earth ◽  
Initial And Boundary Conditions ◽  
Time Existence ◽  
The Magnetic Field

In this paper we study the system governing flows in the magnetic field within the earth. The system is similar to the magnetohydrodynamic (MHD) equations. For initial data in spaceLp, we obtained the local in time existence and uniqueness ofweak solutions of the system subject to appropriate initial and boundary conditions.

Numerical simulation of near-Alfven MHD flows relaxation with a longitudinal magnetic field

2015 ◽  
Vol 81 (3) ◽  
Author(s):  
Evgeniy V. Styopin
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Longitudinal Magnetic Field ◽  
Relaxation Processes ◽  
Plasma Velocity ◽  
Opposite Inequality ◽  
Magnetohydrodynamic Flows ◽  
Longitudinal Plasma ◽  
Nozzle Type ◽  
Alfven Velocity

Stationary magnetohydrodynamics flows in nozzle-type channels in the presence of a longitudinal magnetic field are divided into three significantly different classes: super-Alfven flows in which the longitudinal plasma velocity is higher than the Alfven velocity calculated by a longitudinal magnetic field, sub-Alfven flows – with the opposite inequality, and Alfven flows in which the longitudinal plasma velocity coincides with the Alfven velocity over the entire length of the channel and the plasma density has a constant value. In the present work, stationary Alfven and close to Alfven magnetohydrodynamic flows obtained by using a numerical modeling of their relaxation processes in coaxial channels in the presence of a longitudinal magnetic field are considered.

Математическое описание и анализ сигнала виброиндукционного преобразователя при воздействии нормальной составляющей магнитных потоков рассеяния над дефектным участком

2021 ◽  
Vol 7 ◽  
pp. 19-27
Author(s):  
Ю.Л. Николаев ◽  
П.Н. Шкатов ◽  
Э.Ф. Ахметшина ◽  
А.А. Саморуков
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Initial Data ◽  
Vibration Frequency ◽  
Magnetic Field Intensity ◽  
Theoretical Research ◽  
Leakage Magnetic Field ◽  
Induction Transducer ◽  
Experimental Researches ◽  
Defective Area

Theoretical and experimental researches of vibration-induction transducer (VIT) outlet signal formed during exposure to normal leakage magnetic field intensity component Hn over the defective area were carried out. Theoretical research is based on an assumption that VIT signal is a trigonometric series that is limited by first five harmonics. As initial data for mathematical model creation, well-known conformities for Hn distribution over the defective area were used. Based on acquired mathematical model conformities of VIT signal harmonical composition permutation during its movement over the defective area with varying amplitudes and vibration frequency were found. Theoretical research results were proven experimentally. Moreover, additional possibilities of this way of magnetic testing are shown in comparison with conventional ones.

scholarly journals Darcy's law and diffusion for a two-fluid Euler–Maxwell system with dissipation

2015 ◽  
Vol 25 (11) ◽  
pp. 2089-2151 ◽  
Author(s):  
Renjun Duan ◽  
Qingqing Liu ◽  
Changjiang Zhu
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Frequency Domain ◽  
Large Time ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Time Behavior ◽  
Maxwell System ◽  
The Magnetic Field ◽  
Two Fluid

This paper is concerned with the large-time behavior of solutions to the Cauchy problem on the two-fluid Euler–Maxwell system with dissipation when initial data are around a constant equilibrium state. The main goal is the rigorous justification of diffusion phenomena in fluid plasma at the linear level. Precisely, motivated by the classical Darcy's law for the nonconductive fluid, we first give a heuristic derivation of the asymptotic equations of the Euler–Maxwell system in large time. It turns out that both the density and the magnetic field tend time-asymptotically to the diffusion equations with diffusive coefficients explicitly determined by given physical parameters. Then, in terms of the Fourier energy method, we analyze the linear dissipative structure of the system, which implies the almost exponential time-decay property of solutions over the high-frequency domain. The key part of the paper is the spectral analysis of the linearized system, exactly capturing the diffusive feature of solutions over the low-frequency domain. Finally, under some conditions on initial data, we show the convergence of the densities and the magnetic field to the corresponding linear diffusion waves with the rate [Formula: see text] in L2-norm and also the convergence of the velocities and the electric field to the corresponding asymptotic profiles given in the sense of the generalized Darcy's law with the faster rate [Formula: see text] in L2-norm. Thus, this work can be also regarded as the mathematical proof of the Darcy's law in the context of collisional fluid plasma.

scholarly journals Sensitivity Analysis and Stabilization for Two Dynamical Systems

2018 ◽  
pp. 33-40
Author(s):  
Frank Etin-Osa Bazuaye
Keyword(s):  
Dynamical System ◽  
Sensitivity Analysis ◽  
Dynamical Systems ◽  
Political Parties ◽  
Initial Data ◽  
Differential Equations ◽  
Democratic Process ◽  
Initial State ◽  
Mathematical Problems ◽  
The Impact

This paper focuses on the sensitivity analysis for two dominant political parties. In contrast to Misra, Bazuaye and Khan, who developed the model without investigating the impact of varying the initial state of political parties on the solution trajectory of each political parties, we have developed a sound numerical algorithm to analyze the impact of change on the initial data on the behavior of the democratic process which is a rare contribution to knowledge. Two Matlab standard solvers for ordinary differential equations, ode45 and ode23, have been utilized to handle these formidable mathematical problems. Our findings indicate that as the initial data varies, the dynamical system describing the interaction between two political parties is stabilized over a period of eight years. As duration increases, the systems get de-stabilized.

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