#7507. Relaxation to Fractional Porous Medium Equation from Euler–Riesz System

October 2026publication date
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Journal’s subject area:
Applied Mathematics;
Engineering (all);
Modeling and Simulation;
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Abstract:
We perform asymptotic analysis for the Euler–Riesz system posed in either Td or Rd in the high-force regime and establish a quantified relaxation limit result from the Euler–Riesz system to the fractional porous medium equation. We provide a unified approach for asymptotic analysis regardless of the presence of pressure in the case of repulsive Riesz interactions, based on the modulated energy estimates, the Wasserstein distance of order 2, and the bounded Lipschitz distance.
Keywords:
Asymptotic analysis; Modulated energy; Porous Medium Equation; Relaxation limit; Riesz interaction

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