TY - JOUR
T1 - Propagation of oscillations in the solutions of 1-D compressible fluid equations
AU - Weinan, E.
N1 - Funding Information:
'Research supported by ARO contract DAAL03-89-K-0039 aod AFOSR-90-0090.
PY - 1992/1/1
Y1 - 1992/1/1
N2 - We study the propagation of initial oscillations in the solutions of one-dimensional inviscid gas dynamic equations and the compressible Navier-Stokes equations. Using multiple scale analysis, we derive the homogenized equations which take the form of an averaged system coupled with a dynamic cell-problem. We prove rigorous error estimates to justify the validity of these equations. We also show that the weak limits of the oscillatory solutions satisfy gas dynamic equations with an equation of state depending on the microstructure of the initial data. Copyright.
AB - We study the propagation of initial oscillations in the solutions of one-dimensional inviscid gas dynamic equations and the compressible Navier-Stokes equations. Using multiple scale analysis, we derive the homogenized equations which take the form of an averaged system coupled with a dynamic cell-problem. We prove rigorous error estimates to justify the validity of these equations. We also show that the weak limits of the oscillatory solutions satisfy gas dynamic equations with an equation of state depending on the microstructure of the initial data. Copyright.
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U2 - 10.1080/03605309208820846
DO - 10.1080/03605309208820846
M3 - Article
AN - SCOPUS:84948502575
VL - 17
SP - 545
EP - 552
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
SN - 0360-5302
IS - 3-4
ER -