The stability of rarefaction wave for Navier–Stokes equations in the half‐line |
| |
Authors: | Xiongfeng Yang |
| |
Institution: | Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China |
| |
Abstract: | 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 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 © 2011 John Wiley & Sons, Ltd. |
| |
Keywords: | half‐line Navier– Stokes equation rarefaction wave |
|
|