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arXiv · 2501.15701

Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases

Feng Shao·Dongyi Wei·Shumao Wang·Zhifei Zhang
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Abstract

In this paper, we prove the blow-up of the $3$-D isentropic compressible Navier-Stokes equations for the adiabatic exponent $\gamma=5/3$, which corresponds to the law of monatomic gases. This is the degenerate case in the sense of [Merle, Rapha\"el, Rodnianski and Szeftel, Ann. of Math. (2), 196 (2022), 567-778; Ann. of Math. (2), 196 (2022), 779-889]. Motivated by these breakthrough works, we first establish the existence of a sequence of smooth, self-similar imploding solutions to the compressible Euler equations for $\gamma=5/3$. Subsequently, we utilize these self-similar profiles to construct smooth, asymptotically self-similar blow-up solutions to the compressible Navier-Stokes equations for monatomic gases.

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Feng Shao, Dongyi Wei, Shumao Wang, Zhifei Zhang. 2025-01-26. Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases. https://arxiv.org/abs/2501.15701

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