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arXiv · 2610.16420

The Inviscid Limit of Viscous Burgers through Shock Formation and Development

Chao Wang·Yueyi Yang·Zhifei Zhang
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Abstract

We study the inviscid limit of the one-dimensional viscous Burgers equation from smooth initial data through nondegenerate shock formation and subsequent shock development. Chaturvedi and Graham \cite{CG} obtained sharp estimates of order $ν^{1/4}$ up to the shock-formation time. We extend their analysis beyond this time, comparing the viscous solution with the inviscid entropy solution evolving from the same initial data. With the shock-formation time normalized to $t=0$, we prove a pointwise error bound on a fixed interval $0\leq t \leq \bar{\varepsilon}$, where $\bar{\varepsilon}>0$ is independent of the viscosity $ν$. The bound consists of a term of order $ν^{1/4}$ and an exponentially localized contribution originating from the viscous shock layer. The proof is based on matching an outer expansion, an inner expansion near the formation point, and a viscous shock-profile expansion. Combined with the results of Chaturvedi and Graham, this yields a quantitative description of the inviscid limit from the initial time through the development of the young shock.

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Chao Wang, Yueyi Yang, Zhifei Zhang. 2026-10-12. The Inviscid Limit of Viscous Burgers through Shock Formation and Development. https://arxiv.org/abs/2610.16420

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