3pm - 4pm
Tuesday 6 February 2018

Symmetric solutions of rescaled Fokker-Planck and Boltzmann equations

Florian Theil (Warwick) will be speaking.

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We study the long-time behavior of symmetric solutions of the nonlinear Boltzmann equation and a closely related nonlinear Fokker-Planck equation. If the symmetry of the solutions corresponds to shear flows the existence of stationary solutions can be ruled out because the energy is not conserved.

After anisotropic re-scaling both equations conserve the energy. We show that the rescaled Boltzmann equation does not admit stationary densities of Maxwellian type (exponentially decaying). For the rescaled Fokker-Planck equation we demonstrate that all solutions converge to a Maxwellian in the long-time limit, however the convergence rate is only algebraic, not exponential.