The stability of rarefaction wave for Navier–Stokes equations in the half-line

✍ Scribed by Xiongfeng Yang

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 235 KB
• Volume: 34
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1445

✦ Synopsis

This paper studies the stability of the rarefaction wave for Navier-Stokes equations in the half-line without any smallness condition. When the boundary value is given for velocity u| x=0 = u -and the initial data have the state (v + ,u + ) at x →+∞, if u -<u + , it is excepted that there exists a solution of Navier-Stokes equations in the half-line, which behaves as a 2-rarefaction wave (v R 2 ,u R 2 )(x/ t)| x 0 as t →+∞. Matsumura-Nishihara have proved it for barotropic viscous flow (Quart. Appl. Math. 2000; 58:69-83). Here, we generalize it to the isentropic flow with more general pressure. Copyright