Submitted Paper

Inserted: 14 jan 2025
Last Updated: 14 jan 2025

Year: 2025

Abstract:

We prove that the solution of the viscous Benjamin--Ono equation converges, as diffusion and dispersion parameters tend to zero (under a suitable balance condition), to the unique entropy solution of the inviscid Burgers equation. The key tool in our proof is Schonbek's $L^p$-compensated compactness method. Specifically, we prove a uniform $L^4$-estimate using a modification of a conserved quantity for the inviscid Benjamin--Ono equation and a suitable differential inequality argument.

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• BO-Limit.pdf