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arXiv · 2606.28936

Hydrodynamic limit from nonlinear Fokker--Planck to barotropic Euler equations

José A. Carrillo·Dowan Koo
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Abstract

The hydrodynamic limit to the barotropic Euler equations, including power-law pressure $P(\rho)=\rho^\gamma$, for a kinetic nonlinear Fokker--Planck equation with degenerate diffusion is established. This extends the well-known result of the derivation of isothermal Euler equations via Fokker--Planck equation with linear diffusion. We establish the asymptotic analysis using the relative entropy method by quantifying error estimates for pressures and employing the generalized Log-Sobolev inequality for degenerate diffusion.

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José A. Carrillo, Dowan Koo. 2026-06-27. Hydrodynamic limit from nonlinear Fokker--Planck to barotropic Euler equations. https://arxiv.org/abs/2606.28936

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