带人工粘性的二维可压欧拉方程强稀疏波的渐近稳定性

Asymptotic stability of strong rarefaction wave for the two-dimensional compressible Euler equation with an artificial viscosity

本文研究了一个带人工粘性的二维可压欧拉方程的解收敛于一维稀疏波的渐近行为.如果初值适当接近一个常数并且它们在x=±!的渐近值被选择,那么解收敛于一维稀疏波.由于不要求稀疏波的小强度,因此作者给出了二维可压欧拉方程强稀疏波的非线性稳定.证明方法利用了一维稀疏波的稳定性结果和L2能量方法.

This paper is concerned with the asymptotic behavior toward one-dimensional rarefaction wave of the solution of two-dimensional compressible Euler equation with an artificial viscosity. The solution is proved to tend toward the one-dimensional rarefaction wave as t→ ∞, provided that the initial data are suitably close to a constant state and their asymptotic values at x =±∞ are chosen. Since it is not re- quired the strength of the rarefaction wave to be small, the result gives the nonlinear stability of strong rarefaction wave for the two-dimensional compressible Euler equation. The proof is given by the stability results of one-dimensional rarefaction wave and the elementary L2 energy method.