CONTACT DISCONTINUITIES FOR 2-DIMENSIONAL INVISCID COMPRESSIBLE FLOWS IN INFINITELY LONG NOZZLES

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We prove the existence of a subsonic weak solution (u, rho, p) to a steady Euler system in a two-dimensional infinitely long nozzle when prescribing the value of the entropy (= p/rho gamma) at the entrance by a piecewise C-2 function with a discontinuity at a point. Due to the variable entropy condition with a discontinuity at the entrance, the corresponding solution has a nonzero vorticity and contains a contact discontinuity x(2) = g(D)(x(1)). We construct such a solution via Helmholtz decomposition. The key step is to decompose the Rankine-Hugoniot conditions on the contact discontinuity via Helmholtz decomposition so that the compactness of approximated solutions can be achieved. Then we apply the method of iteration to obtain a piecewise smooth subsonic flow with a contact discontinuity and nonzero vorticity. We also analyze the asymptotic behavior of the solution at far field.
Publisher
SIAM PUBLICATIONS
Issue Date
2019
Language
English
Article Type
Article
Citation

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v.51, no.3, pp.1730 - 1760

ISSN
0036-1410
DOI
10.1137/18M1219540
URI
http://hdl.handle.net/10203/280614
Appears in Collection
MA-Journal Papers(저널논문)
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