Stability of noncharacteristic boundary layers in the standing-shock limit
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Abstract:
We investigate one- and multi-dimensional stability of noncharacteristic boundary layers in the limit approaching a standing planar shock wave $\bar U(x_1)$, $x_1>0$, obtaining necessary conditions of (i) weak stability of the limiting shock, (ii) weak stability of the constant layer $u\equiv U_-:=\lim _{z\to -\infty } \bar U(z)$, and (iii) nonnegativity of a modified Lopatinski determinant similar to that of the inviscid shock case. For Lax $1$-shocks, we obtain equally simple sufficient conditions; for $p$-shocks, $p>1$, the situation appears to be more complicated. Using these results, we determine the stability of certain gas dynamical boundary layers, generalizing earlier work of Serre–Zumbrun and Costanzino–Humphreys–Nguyen–Zumbrun.References
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Additional Information
- Kevin Zumbrun
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 330192
- Email: kzumbrun@indiana.edu
- Received by editor(s): September 15, 2008
- Published electronically: July 14, 2010
- Additional Notes: The author’s research was partially supported under NSF grants number DMS-0070765 and DMS-0300487.
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 6397-6424
- MSC (2010): Primary 35Q35; Secondary 35B35
- DOI: https://doi.org/10.1090/S0002-9947-2010-05213-4
- MathSciNet review: 2678980