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Yuri Trakhinin - One of the best experts on this subject based on the ideXlab platform.
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on the viscous and inviscid stability of magnetohydrodynamic shock waves
Physica D: Nonlinear Phenomena, 2008Co-Authors: Heinrich Freistuhler, Yuri TrakhininAbstract:We study the viscous and inviscid stability of shock waves in barotropic and full Magnetohydrodynamics. We show that there are magnetohydrodynamic shock waves that are one-dimensionally stable as viscous shock profiles while they are multidimensionally strongly unstable as planar shock discontinuities.
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Stability of incompressible current-vortex sheets
Journal of Mathematical Analysis and Applications, 2008Co-Authors: Yuri TrakhininAbstract:Abstract We revisit the study in [Y. Trakhinin, On the existence of incompressible current-vortex sheets: study of a linearized free boundary value problem, Math. Methods Appl. Sci. 28 (2005) 917–945] where an energy a priori estimate for the linearized free boundary value problem for planar current-vortex sheets in ideal incompressible Magnetohydrodynamics was proved for a part of the whole stability domain found a long time ago in [S.I. Syrovatskij, The stability of tangential discontinuities in a magnetohydrodynamic medium, Zh. Eksper. Teor. Fiz. 24 (1953) 622–629 (in Russian); W.I. Axford, Note on a problem of magnetohydrodynamic stability, Canad. J. Phys. 40 (1962) 654–655]. In this paper we derive an a priori estimate in the whole stability domain. The crucial point in deriving this estimate is the construction of a symbolic symmetrizer for a nonstandard elliptic problem for the small perturbation of total pressure. This symmetrizer is an analogue of Kreiss' type symmetrizers. As in hyperbolic theory, the failure of the uniform Lopatinski condition, i.e., the fact that current-vortex sheets are only weakly (neutrally) stable yields loss of derivatives in the energy estimate. The result of this paper is a necessary step to prove the local-in-time existence of stable nonplanar incompressible current-vortex sheets by a suitable Nash–Moser type iteration scheme.
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Existence of Compressible Current-Vortex Sheets: Variable Coefficients Linear Analysis
Archive for Rational Mechanics and Analysis, 2005Co-Authors: Yuri TrakhininAbstract:We study the initial-boundary value problem resulting from the linearization of the equations of ideal compressible Magnetohydrodynamics and the Rankine-Hugoniot relations about an unsteady piecewise smooth solution. This solution is supposed to be a classical solution of the system of Magnetohydrodynamics on either side of a surface of tangential discontinuity (current-vortex sheet). Under some assumptions on the unperturbed flow, we prove an energy a priori estimate for the linearized problem. Since the tangential discontinuity is characteristic, the functional setting is provided by the anisotropic weighted Sobolev space W _2^1,^ σ . Despite the fact that the constant coefficients linearized problem does not meet the uniform Kreiss-Lopatinskii condition, the estimate we obtain is without loss of smoothness even for the variable coefficients problem and nonplanar current-vortex sheets. The result of this paper is a necessary step in proving the local-in-time existence of current-vortex sheet solutions of the nonlinear equations of Magnetohydrodynamics.
Song Jiang - One of the best experts on this subject based on the ideXlab platform.
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incompressible limit of the nonisentropic ideal magnetohydrodynamic equations
Siam Journal on Mathematical Analysis, 2016Co-Authors: Song JiangAbstract:We study the incompressible limit of the compressible nonisentropic ideal magnetohydrodynamic equations with general initial data in the whole space $\mathbb{R}^d$ ($d=2,3$). We first establish the existence of classic solutions on a time interval independent of the Mach number. Then, by deriving uniform a priori estimates, we obtain the convergence of the solution to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero.
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convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations
arXiv: Analysis of PDEs, 2013Co-Authors: Song JiangAbstract:The full compressible magnetohydrodynamic equations can be derived formally from the complete electromagnetic fluid system in some sense as the dielectric constant tends to zero. This process is usually referred as magnetohydrodynamic approximation in physical books. In this paper we justify this singular limit rigorously in the framework of smooth solutions for well-prepared initial data.
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incompressible limit of the non isentropic ideal magnetohydrodynamic equations
arXiv: Analysis of PDEs, 2013Co-Authors: Song JiangAbstract:We study the incompressible limit of the compressible non-isentropic ideal magnetohydrodynamic equations with general initial data in the whole space $\mathbb{R}^d$ ($d=2,3$). We first establish the existence of classic solutions on a time interval independent of the Mach number. Then, by deriving uniform a priori estimates, we obtain the convergence of the solution to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero.
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low mach number limit for the multi dimensional full magnetohydrodynamic equations
arXiv: Analysis of PDEs, 2011Co-Authors: Song JiangAbstract:The low Mach number limit for the multi-dimensional full magnetohydrodynamic equations, in which the effect of thermal conduction is taken into account, is rigorously justified in the framework of classical solutions with small density and temperature variations. Moreover, we show that for sufficiently small Mach number, the compressible magnetohydrodynamic equations admit a smooth solution on the time interval where the smooth solution of the incompressible magnetohydrodynamic equations exists. In addition, the low Mach number limit for the ideal magnetohydrodynamic equations with small entropy variation is also investigated. The convergence rates are obtained in both cases.
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incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions
arXiv: Analysis of PDEs, 2010Co-Authors: Song JiangAbstract:This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions. It is rigorously shown that the weak solutions of the compressible magnetohydrodynamic equations converge to the strong solution of the viscous or inviscid incompressible magnetohydrodynamic equations as long as the latter exists both for the well-prepared initial data and general initial data. Furthermore, the convergence rates are also obtained in the case of the well-prepared initial data.
Dehua Wang - One of the best experts on this subject based on the ideXlab platform.
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local well posedness and low mach number limit of the compressible magnetohydrodynamic equations in critical spaces
Kinetic and Related Models, 2016Co-Authors: Dehua WangAbstract:The local well-posedness and low Mach number limit are considered for the multi-dimensional isentropic compressible viscous magnetohydrodynamic equations in critical spaces. First the local well-posedness of solution to the viscous magnetohydrodynamic equations with large initial data is established. Then the low Mach number limit is studied for general large data and it is proved that the solution of the compressible magnetohydrodynamic equations converges to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero. Moreover, the convergence rates are obtained.
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low mach number limit of viscous compressible magnetohydrodynamic flows
arXiv: Analysis of PDEs, 2009Co-Authors: Dehua WangAbstract:The relationship between the compressible magnetohydrodynamic flows with low Mach number and the incompressible magnetohydrodynamic flows is investigated. More precisely, the convergence of weak solutions of the compressible isentropic viscous magnetohydrodynamic equations to the weak solutions of the incompressible viscous magnetohydrodynamic equations is proved as the density becomes constant and the Mach number goes to zero, that is, the corresponding incompressible limits are justified when the spatial domain is a periodic domain, the whole space, or a bounded domain.
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compactness of weak solutions to the three dimensional compressible magnetohydrodynamic equations
arXiv: Analysis of PDEs, 2009Co-Authors: Xianpeng Hu, Dehua WangAbstract:The compactness of weak solutions to the magnetohydrodynamic equations for the viscous, compressible, heat conducting fluids is considered in both the three-dimensional space $\R^3$ and the three-dimensional periodic domains. The viscosities, the heat conductivity as well as the magnetic coefficient are allowed to depend on the density, and may vanish on the vacuum. This paper provides a new idea to show the compactness of solutions of viscous, compressible, heat conducting magnetohydrodynamic flows, derives a new entropy identity, and shows that the limit of a sequence of weak solutions is still a weak solution to the compressible magnetohydrodynamic equations.
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compactness of weak solutions to the three dimensional compressible magnetohydrodynamic equations
Journal of Differential Equations, 2008Co-Authors: Xianpeng Hu, Dehua WangAbstract:Abstract The compactness of weak solutions to the magnetohydrodynamic equations for the viscous, compressible, heat conducting fluids is considered in both the three-dimensional space R 3 and the three-dimensional periodic domains. The viscosities, the heat conductivity as well as the magnetic coefficient are allowed to depend on the density, and may vanish on the vacuum. This paper provides a different idea from [X. Hu, D. Wang, Global solutions to the three-dimensional full compressible magnetohydrodynamic flows, Comm. Math. Phys. (2008), in press] to show the compactness of solutions of viscous, compressible, heat conducting magnetohydrodynamic flows, derives a new entropy identity, and shows that the limit of a sequence of weak solutions is still a weak solution to the compressible magnetohydrodynamic equations.
A S Petrosyan - One of the best experts on this subject based on the ideXlab platform.
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subgrid scale modeling for the study of compressible magnetohydrodynamic turbulence in space plasmas
Physics-Uspekhi, 2014Co-Authors: A A Chernyshov, K V Karelsky, A S PetrosyanAbstract:A state-of-the-art review is given of research by computing physics methods on compressible magnetohydrodynamic turbulence in space plasmas. The presence of magnetic fields and compressibility in this case makes space plasma turbulence much less amenable to direct numerical simulations than a neutral incompressible fluid. The large eddy simulation method is discussed, which was developed as an alternative to direct modeling and which filters the initial magnetohydrodynamic equations and uses the subgrid-scale modeling of universal small-scale turbulence. A detailed analysis is made of both the method itself and different subgrid-scale parametrizations for compressible magnetohydrodynamic turbulent flows in polytropic and heat-conducting plasmas. The application of subgrid-scale modeling to study turbulence in the local interstellar medium and the scale-invariant spectra of magnetohydrodynamic turbulence are discussed.
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modeling of compressible magnetohydrodynamic turbulence in electrically and heat conducting fluid using large eddy simulation
Physics of Fluids, 2008Co-Authors: A A Chernyshov, K V Karelsky, A S PetrosyanAbstract:Many electrically and heat conducting fluid flows cannot be described within the framework of incompressible medium or by compressible magnetohydrodynamic equations on the assumption of polytropic (or adiabatic) process. Therefore, we consider a heat conducting compressible fluid with the use of an energy equation. Application of large eddy simulation approach to heat conducting compressible Magnetohydrodynamics is considered. The system of the filtered magnetohydrodynamic equations with the total energy equation using the mass-weighted filtering procedure has been obtained. It is shown that novel subgrid-scale terms arise in the Favre-filtered equations due to the presence of a magnetic field in the total energy equation. Parametrizations of these extra terms are developed. In order to derive these subgrid-scale terms, we use an approach based on generalized central moments. Computations at various Mach numbers are made for decaying compressible magnetohydrodynamic turbulence. The obtained numerical larg...
Paul Bellan - One of the best experts on this subject based on the ideXlab platform.
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dynamic and stagnating plasma flow leading to magnetic flux tube collimation
Physical Review Letters, 2005Co-Authors: Setthivoine You, G S Yun, Paul BellanAbstract:Highly collimated, plasma-filled magnetic-flux tubes are frequently observed on galactic, stellar, and laboratory scales. We propose that a single, universal magnetohydrodynamic pumping process explains why such collimated, plasma-filled magnetic-flux tubes are ubiquitous. Experimental evidence from carefully diagnosed laboratory simulations of astrophysical jets confirms this assertion and is reported here. The magnetohydrodynamic process pumps plasma into a magnetic-flux tube and the stagnation of the resulting flow causes this flux tube to become collimated.
