Mathematical Physics

    

A Transport-Diffusion Kinetic Equation

Authors: Payam Danesh, Raoul Bianchetti

This paper studies a linear kinetic equation on a periodic phase space with free transport in position and Ornstein-Uhlenbeck relaxation in velocity. The equation is formulated in the weighted Hilbert space associated with the Maxwellian equilibrium. In that setting, the paper establishes the dissipation identity, conservation of mass, semigroup well-posedness, microscopic coercivity in velocity, and exponential convergence to equilibrium on the zeromass subspace. The spatially homogeneous problem is treated separately, where the entropy law and exponential entropy decay follow directly from the Gaussian logarithmic Sobolev inequality. A final numerical section presents a Fourier-Hermite discretization and illustrates the same relaxation mechanism at the level of decay curves, spectral localization, and density profiles.

Comments: 16 Pages.

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[v1] 2026-04-23 09:09:28

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