scholarly journals One component regularity criteria for the axially symmetric MHD-Boussinesq system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zijin Li ◽  
Xinghong Pan
Keyword(s):  
Magnetic Field ◽  
Blow Up ◽  
A Priori ◽  
Strong Solutions ◽  
Boussinesq System ◽  
Regularity Criteria ◽  
Axially Symmetric ◽  
Magnetic Resistivity ◽  
Boussinesq Systems ◽  
The Magnetic Field

<p style='text-indent:20px;'>In this paper, we consider regularity criteria of a class of 3D axially symmetric MHD-Boussinesq systems without magnetic resistivity or thermal diffusivity. Under some Prodi-Serrin type critical assumptions on the horizontal angular component of the velocity, we will prove that strong solutions of the axially symmetric MHD-Boussinesq system can be smoothly extended beyond the possible blow-up time <inline-formula><tex-math id="M1">\begin{document}$ T_\ast $\end{document}</tex-math></inline-formula> if the magnetic field contains only the horizontal swirl component. No a priori assumption on the magnetic field or the temperature fluctuation is imposed.</p>

scholarly journals Two-fluid simulations of the magnetic field evolution in neutron star cores in the weak-coupling regime

2020 ◽  
Vol 498 (2) ◽  
pp. 3000-3012 ◽  
Author(s):  
F Castillo ◽  
A Reisenegger ◽  
J A Valdivia
Keyword(s):  
Magnetic Field ◽  
Neutron Star ◽  
Charged Particles ◽  
Stable Stratification ◽  
Composition Gradient ◽  
Axially Symmetric ◽  
Drag Forces ◽  
Degeneracy Pressure ◽  
The Magnetic Field ◽  
Two Fluid

ABSTRACT In a previous paper, we reported simulations of the evolution of the magnetic field in neutron star (NS) cores through ambipolar diffusion, taking the neutrons as a motionless uniform background. However, in real NSs, neutrons are free to move, and a strong composition gradient leads to stable stratification (stability against convective motions) both of which might impact on the time-scales of evolution. Here, we address these issues by providing the first long-term two-fluid simulations of the evolution of an axially symmetric magnetic field in a neutron star core composed of neutrons, protons, and electrons with density and composition gradients. Again, we find that the magnetic field evolves towards barotropic ‘Grad–Shafranov equillibria’, in which the magnetic force is balanced by the degeneracy pressure gradient and gravitational force of the charged particles. However, the evolution is found to be faster than in the case of motionless neutrons, as the movement of charged particles (which are coupled to the magnetic field, but are also limited by the collisional drag forces exerted by neutrons) is less constrained, since neutrons are now allowed to move. The possible impact of non-axisymmetric instabilities on these equilibria, as well as beta decays, proton superconductivity, and neutron superfluidity, are left for future work.

scholarly journals High-energy collision of particles in the magnetic field far from black holes

2014 ◽  
Vol 29 (29) ◽  
pp. 1450151
Author(s):  
O. B. Zaslavskii
Keyword(s):  
Magnetic Field ◽  
Black Hole ◽  
Center Of Mass ◽  
High Energy ◽  
Axially Symmetric ◽  
High Energy Collision ◽  
Mass Frame ◽  
Symmetric Black Hole ◽  
Rotating Star ◽  
The Magnetic Field

We consider collision of two particles in the axially symmetric black hole metric in the magnetic field. If the value of the angular momentum |L| of one particles grows unbound (but its Killing energy remains fixed) one can achieve unbound energy in the center-of-mass frame E c.m. In the absence of the magnetic field, collision of this kind is known to happen in the ergoregion. However, if the magnetic field strength B is also large, with the ratio |L|/B being finite, large E c.m. can be achieved even far from a black hole, in the almost flat region. Such an effect also occurs in the metric of a rotating star.

On the theory of magneto-sound double simple waves

2008 ◽  
Vol 74 (4) ◽  
pp. 455-471 ◽  
Author(s):  
DAVY D. TSKHAKAYA ◽  
HOMAYOON ESHRAGHI
Keyword(s):  
Magnetic Field ◽  
Wave Solution ◽  
Blow Up ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Simple Wave ◽  
Initial Distribution ◽  
Relativistic Plasmas ◽  
The One ◽  
The Magnetic Field

AbstractA two-dimensional double simple wave solution is given for both weakly and highly magnetized non-relativistic plasmas moving across the magnetic field. The dependence of the density and the magnetic field on the two independent phases, namely, components of the fluid velocity, is derived. It is shown that initial spatial distributions must satisfy a definite equation whose solution determines a special category for initial conditions. The time of blow up for any fixed value of the pair phase is found. A large general class of solutions for initial distributions is obtained. For any chosen initial distribution, the physical plane of flow at any instant of time splits into two regions, one forbidden and the other permitted. These regions are obtained numerically at a typical time for a special initial distribution. For this double wave solution, differential equations for streamlines and fluid trajectories are derived. Only for the simplest cases can the corresponding curves be completely integrated and these are given in this paper. The results are qualitatively similar to the one-dimensional case derived by Stenflo and Shukla.

Gravitationsinstabilitäten eines Plasmas bei differentieller Rotation

1967 ◽  
Vol 22 (4) ◽  
pp. 431-437
Author(s):  
R. Ebert
Keyword(s):  
Magnetic Field ◽  
Differential Rotation ◽  
Wave Length ◽  
Critical Value ◽  
Unstable Wave ◽  
Simultaneous Action ◽  
Axially Symmetric ◽  
Gas Density ◽  
Axis Of Rotation ◽  
The Magnetic Field

In this paper an instability calculation is given for an axially symmetric gas distribution which has a differential rotation and in which a magnetic field is present. It is a generalization of similar calculations given by CHANDRASEKHAR and BEL and SCHATZMAN. The generalization becomes necessary for the study of problems of the formation of planetary systems, and star formation.The instability conditions and the critical wave lengths are calculated for plane-wave-like disturbances. For disturbances running perpendicularly to the axis of rotation instability can occur only if the gas density exceeds a critical value which depends on the differential rotation at the considered distance only as long as pressure gradients and gradients of the magnetic field strength are negligible. If the gas density exceeds this critical value the shortest unstable wave length is proportional to the square root of vT2+vB2, where vT means the velocity of sound and vB the ALFVÉN-velocity.For disturbances running parallel to the axis of rotation in addition to the JEANS instability a new type of instability occurs due to the simultaneous action of the magnetic field and the differential rotation; for rigid rotation this instability vanishes.

scholarly journals The Cauchy Problem for a Weakly Dissipative 2-Component Camassa-Holm System

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Sen Ming ◽  
Han Yang ◽  
Yonghong Wu
Keyword(s):  
Wave Breaking ◽  
Blow Up ◽  
A Priori Estimates ◽  
A Priori ◽  
Strong Solutions ◽  
Well Posedness ◽  
Priori Estimates ◽  
The Cauchy Problem ◽  
Blow Up Rate ◽  
Global Existence Result

The weakly dissipative 2-component Camassa-Holm system is considered. A local well-posedness for the system in Besov spaces is established by using the Littlewood-Paley theory and a priori estimates for the solutions of transport equation. The wave-breaking mechanisms and the exact blow-up rate of strong solutions to the system are presented. Moreover, a global existence result for strong solutions is derived.

ON A NONLINEAR MAXWELL'S SYSTEM IN QUASI-STATIONARY ELECTROMAGNETIC FIELDS

2004 ◽  
Vol 14 (10) ◽  
pp. 1521-1539 ◽  
Author(s):  
HONG-MING YIN
Keyword(s):  
Magnetic Field ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Blow Up ◽  
Growth Conditions ◽  
System Generator ◽  
Conductive Medium ◽  
Maxwell’S System ◽  
Displacement Currents ◽  
The Magnetic Field

In this paper we study the motion of a magnetic field H in a conductive medium Ω⊂R3under the influence of a system generator. By neglecting displacement currents, the magnetic field satisfies a nonlinear Maxwell's system: Ht+∇×[ρ(x,t)∇×H]=f(|H|)H, where f(|H|)H represents the magnetic currents depending upon the strength of H. We prove that under appropriate initial and boundary conditions, the system has a global solution and the solution is also unique. Moreover, we show that the solution H will blow up in finite time if f(s) satisfies certain growth conditions. Finally, we generalize the results to the problem associated with a nonlinear boundary condition.

scholarly journals Numerical simulations of the emerging plasma blob into a solar coronal hole

2019 ◽  
Vol 489 (2) ◽  
pp. 2769-2774 ◽  
Author(s):  
Anamaría Navarro ◽  
K Murawski ◽  
D Wójcik ◽  
F D Lora-Clavijo
Keyword(s):  
Magnetic Field ◽  
Coronal Hole ◽  
Complex Dynamics ◽  
Hot Plasma ◽  
Magnetic Resistivity ◽  
Plasma Blob ◽  
Parametric Studies ◽  
Magnetic Plasma ◽  
The Magnetic Field ◽  
Solar Coronal

ABSTRACT We numerically simulate emergence of a magnetic plasma blob into a solar coronal hole. This blob may be associated with granulation and therefore it has a weak magnetic field. Two-dimensional simulations are performed using the magnus code which solves magnetohydrodynamic equations, taking into account magnetic resistivity and thermal conduction. As a result of the interaction of the emerging blob with the ambient plasma, the magnetic lines experience reconnection with the blob getting flattened and deformed with time. Additionally, this process launches a vertical outflow of hot plasma and the chromosphere in its response increases its temperature. We perform parametric studies by varying the magnitude of the magnetic field of the blob and observing the net heating of the chromosphere. These studies are inspired by realistic simulations of granulation made with the use of two-fluid joanna code. In these simulations a number of magnetic blobs are detected in the convection zone and in the photosphere. From the numerical results, we conclude that as a result of granulation operating in a solar quiet region the emerging blob may trigger very complex dynamics in the upper regions of the solar atmosphere, and the associated outflows may be a source of heating of the chromosphere and possibly the solar corona.

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