This article is cited in 12 scientific papers (total in 12 papers)
Stability of a supersonic flow about a wedge with weak shock wave
A. M. Blokhin, D. L. Tkachev
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
It is known that the problem of finding the streamlines of a stationary supersonic flow
of a nonviscous nonheat-conducting gas in thermodynamical equilibrium past an infinite plane
wedge (with a sufficiently small angle at the vertex) in theory has two solutions: a strong shock wave solution (the velocity behind the front of the shock wave is subsonic) and a weak shock wave solution (the velocity behind the front of the shock wave is generally speaking supersonic). In the present paper it is shown
for a linear approximation to this problem that the weak shock wave solution is asymptotically stable in the sense of Lyapunov. Moreover, it is shown that for initial data with compact support the solution of the mixed linear problem converges in finite time to the zero solution. In the case of linear approximation these
results complete the verification of the well-known Courant-Friedrichs conjecture that the strong
shock wave solution is unstable, whereas the weak shock wave solution is asymptotically stable in the sense of Lyapunov.
Bibliography: 39 titles.
weak shock wave, asymptotic stability (in the sense of Lyapunov).
Author to whom correspondence should be addressed
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Sbornik: Mathematics, 2009, 200:2, 157–184
MSC: 76J20, 34D20
Received: 20.05.2008 and 26.11.2008
A. M. Blokhin, D. L. Tkachev, “Stability of a supersonic flow about a wedge with weak shock wave”, Mat. Sb., 200:2 (2009), 3–30; Sb. Math., 200:2 (2009), 157–184
Citation in format AMSBIB
\by A.~M.~Blokhin, D.~L.~Tkachev
\paper Stability of a~supersonic flow about a~wedge with weak shock wave
\jour Mat. Sb.
\jour Sb. Math.
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M. Darwish, F. Moukalled, “A fully coupled Navier–Stokes solver for fluid flow at all speeds”, Numerical Heat Transfer, Part B: Fundamentals, 65:5 (2014), 410–444
A. N. Kraiko, K. S. P'yankov, Ye. A. Yakovlev, “The flow of a supersonic ideal gas with “weak” and “strong” shocks over a wedge”, J. Appl. Math. Mech., 78:4 (2014), 318–330
A. M. Blokhin, D. L. Tkachev, “Stability of a supersonic flow over a wedge containing a weak shock wave satisfying the Lopatinski condition”, J. Hyberbolic Differ. Equ., 11:2 (2014), 215–248
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A. M. Blokhin, D. L. Tkachev, “Stability of a supersonic flow past a wedge with adjoint weak neutrally stable shock wave”, Siberian Adv. Math., 27:2 (2017), 77–102
Blokhin A., Tkachev D., “Linear stability of a weak shock wave appearing in flow over an infinite plane wedge (Lopatinski condition is fulfilled on the shock)”, INTERNATIONAL CONFERENCE ON THE METHODS OF AEROPHYSICAL RESEARCH (ICMAR 2016): Proceedings of the 18th International Conference on the Methods of Aerophysical Research (Perm, Russia, 27 June–3 July 2016), AIP Conference Proceedings, 1770, ed. Fomin V., Amer Inst Physics, 2016, 030080
Tkachev D.L., Blokhin A.M., “The problem of flow about infinite plane wedge with inviscous non-heat-conducting gas. Linear stability of a weak shock wave”, 2016 Days on Diffraction (DD) (St.Petersburg, Russia), eds. Motygin O., Kiselev A., Kapitanova P., Goray L., Kazakov A., Kirpichnikova A., IEEE, 2016, 410–415
Blokhin A.M., Tkachev D.L., “Local Well-Posedness in the Problem of Flow About Infinite Plane Wedge With Inviscous Non-Heat-Conducting Gas”, Proceedings of the International Conference Days on Diffraction (Dd) 2017, eds. Motygin O., Kiselev A., Goray L., Suslina T., Kazakov A., Kirpichnikova A., IEEE, 2017, 62–67
E. V. Semenko, T. I. Semenko, “The shock front asymptotics in the linear problem of shock wave”, Sib. elektron. matem. izv., 15 (2018), 950–970
A. M. Blokhin, D. L. Tkachev, A. V. Yegitov, “Local solvability of the problem of the van der Waals gas flow around an infinite plane wedge in the case of a weak shock wave”, Siberian Math. J., 59:6 (2018), 960–982
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