Spatially homogeneous solutions of the Vlasov-Nordstrom-Fokker-Planck system

• The Vlasov-Nordstrom-Fokker-Planck system describes the evolution of self-gravitating matter experiencing collisions with a fixed background of particles in the framework of a relativistic scalar theory of gravitation. We study the spatially-homogeneous system and prove global existence and uniqueness of solutions for the corresponding initial value problem in three momentum dimensions. Additionally, we study the long time asymptotic behavior of the system and prove that even in the absence of friction, solutions possess a non-trivial asymptotic profile. An exact formula for the long time limit of the particle density is derived in the ultra-relativistic case.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Vlasov-Nordstrom

Fokker-Planck equation

Spatially homogeneous

Global existence

Ultra-

STEADY-STATES

EXISTENCE

BEHAVIOR

EQUATION

Mathematics

Global existence

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