Large-time behavior for spherically symmetric flow of viscous polytropic gas in exterior unbounded domain with large initial data

2014/05/03 by Zhilei Liang, Liang, Zhilei · 1 citation
Mathematics · Engineering · #Navier-Stokes equation solutions #Computational Fluid Dynamics and Aerodynamics #Gas Dynamics and Kinetic Theory

paper · pdf · doi:10.48550/arxiv.1405.0569

Abstract

This paper deals with the spherically symmetric flow of compressible viscous and polytropic ideal fluid in unbounded domain exterior to a ball in ℝⁿ with n≥2. We show that the global solutions are convergent as time goes to infinity. The critical step is obtaining the point-wise bound of the specific volume v(x,t) and the absolute temperature θ(x,t) from up and below both for x and t. Note that the initial data can be arbitrarily large and, compared with \citenn, our method applies to the spatial dimension n=2. The proof is based on the elementary energy methods.

Cited by

• Global Spherical Symmetric Flows for a Viscous Radiative and Reactive Gas in an Exterior Domain with Large Initial Data

Related

• Global Spherical Symmetric Flows for a Viscous Radiative and Reactive Gas in an Exterior Domain with Large Initial Data
• Large-Time Behavior of Solutions to Compressible Navier-Stokes System in Unbounded Domains with Degenerate Heat-Conductivity and Large Data
• Large-time behaviour of the spherically symmetric solution to an outflow problem for isentropic model of compressible viscous fluid
• Existence of radially symmetric stationary solutions for viscous and Heat-conductive ideal Gas
• Global Spherically Symmetric Solutions of the Multidimensional Full Compressible Navier-Stokes Equations with Large Data