Author

Geng Chen

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Preprint Oct 2026

Relative Entropy and the Inviscid Limit for Planar Shocks of the Multi-D Burgers'Equation

In recent work (arXiv:2610.10341), the authors introduced a framework for studying the vanishing viscosity limit for sequences of weak solutions of the multi-dimensional compressible Navier-Stokes equations to planar shocks of the compressible Euler equations. In this paper, we introduce these methods and apply them to...

Geng Chen, Jeffrey Cheng, Alexis F. Vasseur et al. · 0 citations

Review Oct 2026

Uniqueness and stability of planar shock wave to 2D compressible Euler equations in the vanishing viscosity limit of compressible Navier-Stokes equations

It is well known that the compressible Euler equations with planar shock initial data may admit infinitely many entropy weak solutions, as shown by Chiodaroli, De Lellis and Kreml [Comm. Pure Appl. Math. (2015)]. In this paper, we introduce a suitable notion of global-in-time weak solutions to the two-dimensional (2D)...

Geng Chen, Jeffrey Cheng, Alexis F. Vasseur et al. · 1 citation · ⚡1

Preprint Sep 2026

Structurally stable singularities and Lipschitz stable optimal transport metrics for the compressible Euler equations

It is well known that solutions to the compressible Euler equations can develop singularities in finite time. In this paper, we carry out a detailed analysis on behaviors of solutions up to the time of the first singularity for the one-dimensional compressible Euler equations with general smooth initial data. Our main...

Geng Chen, Yan-Bo Hu, Yan-Nan Shen · 0 citations