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The stability of rarefaction wave for Navier–Stokes equations in the half‐line
Author(s) -
Yang Xiongfeng
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1445
Subject(s) - barotropic fluid , mathematics , rarefaction (ecology) , isentropic process , mathematical analysis , stability (learning theory) , flow (mathematics) , boundary value problem , stokes wave , line (geometry) , navier–stokes equations , half line , non dimensionalization and scaling of the navier–stokes equations , mechanics , geometry , compressibility , wave propagation , physics , breaking wave , ecology , quantum mechanics , species diversity , biology , machine learning , computer science
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.