Preprint

Inserted: 24 sep 2026
Last Updated: 24 sep 2026

Year: 2026

Abstract:

We prove that solutions of the Benjamin--Ono--Burgers equation converge to the entropy solution of the inviscid Burgers equation as the viscosity $\varepsilon$ and dispersion $\delta$ tend to zero subject to $\delta=o(\varepsilon)$. This improves the previously known condition $\delta=O(\varepsilon^{3/2})$. The main new ingredient is a local spacetime $L^4$ estimate obtained from the one-dimensional interaction identity associated with the Varadhan functional, applied to the conservation law and its quadratic entropy balance.

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