Details

Alexander V. Bobylev^[a]

On propagation of exponential moments for the Landau kinetic equation

Pages: 31-43
Received: 19 April 2023
Accepted in revised form: 7 August 2023
Mathematics Subject Classification: 82D10, 82C70, 82C31.
Keywords: Landau kinetic equation, radial symmetry, distribution function, power moments, exponential moments.
Author address:
[a]: Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, 125047 Moscow, Russia

Abstract: The paper is devoted to study of asymptotic properties (for large values of energy) of radially symmetric solutions to the spatially homogeneous Landau equation for Coulomb forces. The main result of the paper is the proof of propagation in time of the exponential moment of the third order and some explicit time-dependent estimates of this moment. Roughly speaking, this means that the high energy tails of the form \( \exp[- b(t) v^{k}] \) with some \( k \geq 3 \) are typical for solutions of the Landau equation with initial data having compact support. A comparison with related results for similar kinetic equations is briefly discussed.

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