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Multidimensional stability of large-amplitude Navier-Stokes shocks

Banff International Research Station for Mathematical Innovation and Discovery

Extending results of Humpherys-Lyng-Zumbrun in the one-dimensional case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the multidimensional stability of planar Navier-Stokes shocks across the full range of shock amplitudes, including the infinite-amplitude limit, for monatomic or diatomic ideal gas equations of state and viscosity and heat conduction coefficients constant and in the physical ratios predicted by statistical mechanics, with Mach number $M>1.035$. Our results indicate unconditional stability within the parameter range considered, in agreement with the results of Erpenbeck and Majda in the corresponding inviscid case. Notably, this study includes the first successful numerical Evans computation for multi-dimensional stability of a viscous shock wave. This is joint work with J. Humpherys (BYU) and K. Zumbrun (Indiana).

Mathematics; Partial differential equations; Dynamical systems and ergodic theory; Functional analysis

video/mp4

Author affiliation: University of Wyoming

2017-12-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64112

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/