Local-in-time well-posedness for the regular solution to the 2D full compressible Navier-Stokes equations with degenerate viscosities and heat conductivity

Yue Cao; Xun Jiang

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arXiv · 2504.10094

Local-in-time well-posedness for the regular solution to the 2D full compressible Navier-Stokes equations with degenerate viscosities and heat conductivity

Yue Cao·Xun Jiang

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Abstract

This paper considers the two-dimensional Cauchy problem of the full compressible Navier-Stokes equations with far-field vacuum in $\mathbb{R}^2$, where the viscosity and heat-conductivity coefficients depend on the absolute temperature $θ$ in the form of $θ^ν$ with $ν>0$. Due to the appearance of the vacuum, the momentum equation are both degenerate in the time evolution and spatial dissipation, which makes the study on the well-posedness challenged. By establishing some new singular-weighted (negative powers of the density $ρ$) estimates of the solution, we establish the local-in-time well-posedness of the regular solution with far-field vacuum in terms of $ρ$, the velocity $u$ and the entropy $S$.

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Yue Cao, Xun Jiang. 2025-04-14. Local-in-time well-posedness for the regular solution to the 2D full compressible Navier-Stokes equations with degenerate viscosities and heat conductivity. https://arxiv.org/abs/2504.10094

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