Global solutions to the isentropic compressible Navier-Stokes equations with a class of large initial data

2016/08/23 by Daoyuan Fang, Ting Zhang, Fang, Daoyuan +3 · 2 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1608.06447

openalex publication_date 2016/08/23 · openalex created_date 2016/09/16 · openalex updated_date 2026/08/01

Abstract

In this paper, we consider the global well-posedness problem of the isentropic compressible Navier-Stokes equations in the whole space \R^N with N≥2. In order to better reflect the characteristics of the dispersion equation, we make full use of the role of the frequency on the integrability and regularity of the solution, and prove that the isentropic compressible Navier-Stokes equations admit global solutions when the initial data are close to a stable equilibrium in the sense of suitable hybrid Besov norm. As a consequence, the initial velocity with arbitrary B^\frN2-1_2,1 norm of potential part \Pe^\bot u₀ and large highly oscillating are allowed in our results. The proof relies heavily on the dispersive estimates for the system of acoustics, and a careful study of the nonlinear terms.

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions

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

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