Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions

Technical Report · Mon Mar 01 04:00:00 EST 1993

DOI:https://doi.org/10.2172/7368456· OSTI ID:7368456

Batt, J; Rein, G ^[1]; Morrison, P J ^[2]

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1. Muenchen Univ. (Germany). Mathematisches Inst.
2. Texas Univ., Austin, TX (United States)

Rigorous results on the stability of stationary solutions of the Vlasov-Poisson system are obtained in both the plasma physics and stellar dynamics contexts. It is proven that stationary solutions in the plasma physics (stellar dynamics) case are linearly stable if they are decreasing (increasing) functions of the local, i.e. particle, energy. The main tool in the analysis is the free energy of the system, a conserved quantity. In addition, an appropriate global existence result is proven for the linearized Vlasov-Poisson system and the existence of stationary solutions that satisfy the above stability condition is established.

• Research Organization: Texas Univ., Austin, TX (United States)
• Sponsoring Organization: DOE; USDOE, Washington, DC (United States)
• DOE Contract Number: FG05-80ET53088
• OSTI ID: 7368456
• Report Number(s): DOE/ET/53088-597; IFSR--597; ON: DE93013873
• Country of Publication: United States
• Language: English

Related Subjects

661300 -- Other Aspects of Physical Science-- (1992-)
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700330* -- Plasma Kinetics
Transport
& Impurities-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
BOLTZMANN-VLASOV EQUATION
CHARGE DENSITY
COLLISIONLESS PLASMA
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ENERGY
EQUATIONS
FREE ENERGY
FUNCTIONS
GALAXIES
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
PHYSICAL PROPERTIES
PLASMA
POISSON EQUATION
SPACE
STABILITY
STARS
THERMODYNAMIC PROPERTIES
THREE-DIMENSIONAL CALCULATIONS