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On the asymptotic growth of the solutions of the Vlasov–Poisson system. (English) Zbl 0782.35079
The Vlasov-Poisson equation is the well known integro-differential equation which describes the dynamics of a galaxy or a plasma. Its difficulty is due to the presence of a singular kernel in the integral which defines the Newtonian or Coulomb force, depending upon the case.
In order to study this equation, the author regularizes this kernel by using a perturbation scheme. He proves a global theorem for this modified equation, and then he makes the perturbation parameter tend to zero. Moreover he shows that the velocities of the particles (stars or ions) grow like \(O(t\log^{11/14} t)\) in time.

MSC:
35Q72 Other PDE from mechanics (MSC2000)
85A05 Galactic and stellar dynamics
82D10 Statistical mechanical studies of plasmas
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