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

2025/04/14 by Cao, Yue, Jiang, Xun
#35A01 #35A09 #35B40 #35Q30 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.10094

Abstract

This paper considers the two-dimensional Cauchy problem of the full compressible Navier-Stokes equations with far-field vacuum in ℝ², 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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