Global regularity and incompressible limit of 2D compressible Navier-Stokes equations with large bulk viscosity

2025/06/27 by Liu, Shengquan, Zhang, Jianwen
#35B65 #35Q35 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.22235

Abstract

In this paper, we study the global regularity of large solutions with vacuum to the two-dimensional compressible Navier-Stokes equations on \mathbbT²=ℝ²/ℤ², when the volume (bulk) viscosity coefficient ν is sufficiently large. It firstly fixes a flaw in \cite[Proposition 3.3]Danchin2023, which concerns the ν-independent global t-weighted estimates of the solutions. Amending the proof requires non-trivially mathematical analysis. As a by-product, the incompressible limit with an explicit rate of convergence is shown, when the volume viscosity tends to infinity. In contrast to \cite[Theorem 1.3]Danchin2019 and \cite[Corollary 1.1]DM2017 where vacuum was excluded, the convergence rate of the incompressible limit is obtained for the global solutions with vacuum, based on some t-growth and singular t-weighted estimates.

Citations

• On local strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with vacuum
• Compressible Navier-Stokes equations with ripped density
• The incompressible navier-stokes equations in vacuum
• Compressible Navier-Stokes system : large solutions and incompressible\n limit
• Existence and Blowup Behavior of Global Strong Solutions to the Two-Dimensional Baratropic Compressible Navier-Stokes System with Vacuum and Large Initial Data
• Global Well-Posedness of Classical Solutions with Large Oscillations and Vacuum to the Three-Dimensional Isentropic Compressible Navier-Stokes Equations
• On commutators of singular integrals and bilinear singular integrals

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