Please use this identifier to cite or link to this item: http://repository.vnu.edu.vn/handle/VNU_123/26635
Title: Existence of traveling waves in compressible Euler equations with viscosity and capillarity
Authors: Mai Duc Thanh
Keywords: Compressible Euler equations;Traveling wave;Shock;Viscosity;Capillarity;Equilibria;Asymptotical stability;Lyapunov function;LaSalle’s invariance principle;Attraction domain
Issue Date: 2012
Publisher: PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Citation: ISIKNOWLEDGE
Abstract: Given any Lax shock of the compressible Euler dynamics equations, we show that there exists the corresponding traveling wave of the system when viscosity and capillarity are suitably added. For a traveling wave corresponding to a given Lax shock, the governing viscous–capillary system is reduced to a system of two differential equations of first-order, which admits an asymptotically stable equilibrium point and a saddle point. We then develop the method of estimating attraction domain of the asymptotically stable equilibrium point for the compressible Euler equations and show that the saddle point in fact lies on the boundary of this set. Then, we establish a saddle-to-stable connection by pointing out that there is a stable trajectory leaving the saddle point and entering the attraction domain of the asymptotically stable equilibrium point. This gives us a traveling wave of the viscous–capillary compressible Euler equations.
Description: TNS06836 ; NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS Volume: 75 Issue: 13 Pages: 4884-4895 Published: SEP 2012
URI: http://repository.vnu.edu.vn/handle/VNU_123/26635
http://www.sciencedirect.com/science/article/pii/S0362546X12001320
ISSN: 0362-546X
1873-5215
Appears in Collections:Bài báo của ĐHQGHN trong Web of Science

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