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Su un problema di instabilità gravitazionale di un fluido in presenza di correnti di Hall e di ion slip

Giulio Mattei (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questo lavoro si studia la instabilità gravitazionale di un fluido comprimibile, elettroconduttore, descritto dalle equazioni della magnetofluidodinamica in presenza delle correnti di Hall e di ion slip. Si determina la condizione per la instabilità relativa ad una classe di perturbazioni assialsimmetriche.

Sui moti per eliche circolari in Meccanica dei plasmi

Giulio Mattei (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we extend to Plasma Mechanics the study of the hydrodynamic steady motions in which the streamlines are circular helixes. The plasma is described by the magnetofïuiddynamic equations with the Hall effect. Velocity and magnetic fields (and, in correspondence, the pressure field) that make such motions possible are determined. So a class of exact solutions of the magnetofïuiddynamic equations with the Hall effect is pointed out.

Sull'equilibrio di un plasma radiativo in rotazione. Nota I

Margareta Ignat (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This paper studies the magnetodynamic equilibrium of a radiative, infinitely conducting plasma, undergoing both a rotation motion around a symmetry axis and a motion in the meridian plans. It is assumed that on plasma acts its own gravitation. In the first nota the plasma is considered incompressible; for such a plasma the approximation of a perfect gas is valid.

Sull’equilibrio relativo di un plasma radiativo in rotazione. Nota II

Margareta Ignat (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This paper studies the magnetodynamic equilibrium of a radiative, infinitely conducting plasma, undergoing both a rotation motion around a symmetry axis and a motion in the meridian plans. It is assumed that on plasma acts its own gravitation. In the second note the plasma is supposed to be polytropic and compressible. The stability criterion of such a splasma is also obtained.

The Cauchy problem for the two dimensional Euler–Poisson system

Dong Li, Yifei Wu (2014)

Journal of the European Mathematical Society

The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo [7] first constructed a global smooth irrotational solution by using the dispersive Klein-Gordon effect. It has been conjectured that same results should hold in the two-dimensional case. In our recent work [13], we proved the existence of a family of smooth solutions by constructing the wave operators for the 2D system....

The numerical interface coupling of nonlinear hyperbolic systems of conservation laws : II. The case of systems

Edwige Godlewski, Kim-Claire Le Thanh, Pierre-Arnaud Raviart (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study the theoretical and numerical coupling of two hyperbolic systems of conservation laws at a fixed interface. As already proven in the scalar case, the coupling preserves in a weak sense the continuity of the solution at the interface without imposing the overall conservativity of the coupled model. We develop a detailed analysis of the coupling in the linear case. In the nonlinear case, we either use a linearized approach or a coupling method based on the solution of a Riemann problem. We...

The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: II. The case of systems

Edwige Godlewski, Kim-Claire Le Thanh, Pierre-Arnaud Raviart (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the theoretical and numerical coupling of two hyperbolic systems of conservation laws at a fixed interface. As already proven in the scalar case, the coupling preserves in a weak sense the continuity of the solution at the interface without imposing the overall conservativity of the coupled model. We develop a detailed analysis of the coupling in the linear case. In the nonlinear case, we either use a linearized approach or a coupling method based on the solution of a Riemann problem....

Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping

R. Belaouar, T. Colin, G. Gallice, C. Galusinski (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we study a Zakharov system coupled to an electron diffusion equation in order to describe laser-plasma interactions. Starting from the Vlasov-Maxwell system, we derive a nonlinear Schrödinger like system which takes into account the energy exchanged between the plasma waves and the electrons via Landau damping. Two existence theorems are established in a subsonic regime. Using a time-splitting, spectral discretizations for the Zakharov system and a finite difference scheme for the...

Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping

R. Belaouar, T. Colin, G. Gallice, C. Galusinski (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we study a Zakharov system coupled to an electron diffusion equation in order to describe laser-plasma interactions. Starting from the Vlasov-Maxwell system, we derive a nonlinear Schrödinger like system which takes into account the energy exchanged between the plasma waves and the electrons via Landau damping. Two existence theorems are established in a subsonic regime. Using a time-splitting, spectral discretizations for the Zakharov system and a finite difference scheme for...

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