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arXiv · 2610.25889

Global regularity and sharp decay rates for the one-dimensional hypo-viscous compressible Navier-Stokes equations in critical Besov spaces

Chen Liang·Zhaonan Luo·Zhaoyang Yin
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Abstract

In this paper, we study the global regularity of the one-dimensional hypo-viscous compressible Navier--Stokes equations in the critical Besov spaces, where the initial data are close to the constant equilibrium state. We introduce an effective velocity, constructed as a combination of the density and the velocity, which is used to capture the high-frequency behavior of $a$. By performing elaborate high-frequency and low-frequency estimates together with a bootstrap argument, we obtain global existence for $\frac{1}{2}\leβ<1$. In particular, when $\frac{1}{2}\leβ<\frac{3}{4}$, we also prove the uniqueness of solutions. Furthermore, under an additional low-frequency assumption, we establish the optimal time decay rates.

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Chen Liang, Zhaonan Luo, Zhaoyang Yin. 2026-10-19. Global regularity and sharp decay rates for the one-dimensional hypo-viscous compressible Navier-Stokes equations in critical Besov spaces. https://arxiv.org/abs/2610.25889

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