Global weak solutions and incompressible limit to the isentropic compressible Navier-Stokes equations in the half-plane with ripped density and large initial data

2025/07/04 by Shuai Wang, Guochun Wu, Wang, Shuai +3 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2507.03505

openalex publication_date 2025/07/04 · openalex created_date 2025/10/20 · openalex updated_date 2026/08/02

Abstract

We prove the global existence of weak solutions to the isentropic compressible Navier-Stokes equations with ripped density in the half-plane under a slip boundary condition provided the bulk viscosity coefficient is properly large. Moreover, we show that such solutions converge globally in time to a weak solution of the inhomogeneous incompressible Navier-Stokes equations as the bulk viscosity coefficient tends to infinity. In particular, the large initial data and an initial patch of density as well as a vacuum are allowed. Our method relies on a Desjardins-type logarithmic interpolation inequality and some new techniques based on the effective viscous flux.

Citations

• A new construction of weak solutions to compressible Navier-Stokes equations
• Existence and Exponential Growth of Global Classical Solutions to the Compressible Navier-Stokes Equations with Slip Boundary Conditions in 3D Bounded Domains
• Compressible Navier-Stokes equations with ripped density
• Global large solutions to the two dimensional compressible Navier-Stokes equations
• Global stability of large solutions to the 3D compressible Navier-Stokes equations
• Global solutions to the isentropic compressible Navier-Stokes equations with a class of large initial data
• Compressible Navier-Stokes system : large solutions and incompressible\n limit
• Global Existence of Weak Solutions for Compresssible Navier--Stokes Equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor
• On Imbeddings into Orlicz Spaces and Some Applications

Cited by

• Global weak solutions and incompressible limit to the isentropic compressible Navier-Stokes equations in 2D bounded domains with ripped density and large initial data

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