FORMATION OF SINGULARITY AND SMOOTH WAVE PROPAGATION FOR THE NON-ISENTROPIC COMPRESSIBLE EULER EQUATIONS
2011 ◽
Vol 08
(04)
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pp. 671-690
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Keyword(s):
We define the notion of compressive and rarefactive waves and derive the differential equations describing smooth wave steepening for the compressible Euler equations with a varying entropy profile and general pressure laws. Using these differential equations, we directly generalize Lax's singularity (shock wave) formation results (established in 1964 for hyperbolic systems with two variables) to the 3 × 3 compressible Euler equations for a polytropic ideal gas. Our results are valid globally without restriction on the size of the variation of initial data.
2004 ◽
Vol 175
◽
pp. 125-164
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2021 ◽
Vol 18
(03)
◽
pp. 701-728
2017 ◽
Vol 448
(1)
◽
pp. 245-261
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Keyword(s):
2009 ◽
Vol 16
(3)
◽
pp. 341-364
◽
Keyword(s):
2018 ◽
Vol 15
(04)
◽
pp. 721-730
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Keyword(s):
1999 ◽
Vol 154
◽
pp. 157-169
◽
2015 ◽
Vol 338
(2)
◽
pp. 771-800
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