Asymptotics toward one-dimensional rarefaction wave for the solution of two-dimensional compressible Euler equation with an artificial viscosity

Article type: Research Article

Authors: Hokari, Hisaaki | Matsumura, Akitaka

Affiliations: Department of Mathematics, Kanazawa University, Kanazawa 920-11, Japan | Department of Mathematics, Osaka University, Toyonaka 560, Japan

Abstract: This paper is concerned with the asymptotic behavior toward one-dimensional rarefaction wave for the solution of two-dimensional compressible Euler equation with an artificial viscosity. It is shown that if the initial data are suitably close to a constant state and their asymptotic values at x=±∞ are chosen so that the Riemann problem for the corresponding one-dimensional hyperbolic system admits the weak rarefaction wave, then the solution is proved to tend toward the one-dimensional rarefaction wave as t→+∞. The proof is given by using stability results of one-dimensional rarefaction wave and an elementary L2 energy method.

DOI: 10.3233/ASY-1997-153-404

Journal: Asymptotic Analysis, vol. 15, no. 3-4, pp. 283-298, 1997