Convergence rate of stationary solutions to outflow problem for full Navier–Stokes equations. Issue 7 (19th May 2019)

• Record Type: Journal Article
• Authors: Chen, Yazhou; Hong, Hakho; Shi, Xiaoding
• Is Part Of: Applicable analysis. Volume 98:Issue 7(2019)
• Page Start: 1267
• Page End: 1288
• Publication Date: 2019-05-19
• Subjects: Compressible Navier–Stokes equations -- outflow problem -- stationary solution -- stability -- convergence rate; 35Q30 -- 35B35 -- 35L65 -- 76D33 -- 74J40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1419203
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: This paper is concerned with the large-time behavior of solutions to the outflow problem of full compressible Navier–Stokes equations for the general gas including ideal polytropic gas in the half lineR + = ( 0, ∞ ), where the gas flows out through the boundary. We first give some necessary and sufficient conditions for the existence of the stationary solution with the aid of center manifold theory. We also show the time asymptotic stability of the nondegenerate stationary solution under smallness assumptions on the boundary data and the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the exponential and algebraic decay of the solution toward the supersonic stationary solution is obtained, provided that the initial perturbation belongs to the Sobolev space with exponential and algebraic weight respectively.