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Shock waves for compressible navier‐stokes equations are stable
Author(s) -
Liu TaiPing
Publication year - 1986
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160390502
Subject(s) - shock wave , mathematics , conservation law , compressibility , nonlinear system , energy method , mathematical analysis , perturbation (astronomy) , compressible flow , classical mechanics , mechanics , physics , quantum mechanics
It is shown that shock waves for the compressible Navier‐Stokes equations are nonlinearly stable. A perturbation of a shock wave tends to the shock wave, properly translated in phase, as time tends to infinity. Through the consideration of conservation of mass, momentum and energy we obtain an a priori estimate of the amount of translation of the shock wave and the strength of the linear and nonlinear diffusion waves that arise due to the perturbation. Our techniques include the energy method for parabolic‐hyperbolic systems, the decomposition of waves, and the energy‐characteristic method for viscous conservation laws introduced earlier by the author.