Convex Entropy, Hopf Bifurcation, and Viscous and Inviscid Shock Stability
نویسندگان
چکیده
منابع مشابه
Hopf Bifurcation From Viscous Shock Waves
Using spatial dynamics, we prove a Hopf bifurcation theorem for viscous Lax shocks in viscous conservation laws. The bifurcating viscous shocks are unique (up to time and space translation), exponentially localized in space, periodic in time, and their speed satisfies the Rankine–Hugoniot condition. We also prove an ”exchange of spectral stability” result for superand subcritical bifurcations, ...
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Extending our previous results for artificial viscosity systems, we show, under suitable spectral hypotheses, that shock wave solutions of compressible Navier–Stokes (cNS) and magnetohydrodynamics (MHD) equations undergo Hopf bifurcation to nearby time-periodic solutions. The main new difficulty associated with physical viscosity and the corresponding absence of parabolic smoothing is the need ...
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Combining work of Serre and Zumbrun, Benzoni-Gavage, Serre, and Zumbrun, and Texier and Zumbrun, we propose as a mechanism for the onset of cellular instability of viscous shock and detonation waves in a finite-cross-section duct the violation of the refined planar stability condition of Zumbrun–Serre, a viscous correction of the inviscid planar stability condition of Majda. More precisely, we ...
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ژورنال
عنوان ژورنال: Archive for Rational Mechanics and Analysis
سال: 2015
ISSN: 0003-9527,1432-0673
DOI: 10.1007/s00205-014-0838-6