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arXiv · 2605.00407

Gradient blowup of smooth vacuum solutions to 1D compressible Euler equations

Juhi Jang·Jiaqi Liu·Nader Masmoudi
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Abstract

We consider the isentropic compressible Euler equations in the half-line which govern the motion of gaseous fluids in contact with stationary vacuum boundary. We construct a large class of solutions that are initially smooth and square-integrable, and which, in finite time, transition to $C^{1-\mu}$ regularity for $\mu \in [1/2,1)$ near the boundary, leading to the gradient blowup at the boundary. It is based on stability analysis of self-similar waiting time solutions \cite{JLN2025} recently constructed by the authors.

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Juhi Jang, Jiaqi Liu, Nader Masmoudi. 2026-05-01. Gradient blowup of smooth vacuum solutions to 1D compressible Euler equations. https://arxiv.org/abs/2605.00407

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