Existence of solutions to the transonic pressure-gradient equations of the compressible Euler equations in elliptic regions

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Abstract

We establish the existence of a smooth solution in its elliptic region in the self-similar plane to the pressure-gradient system arisen from the wave-particle splitting of the two-dimensional compressible Euler system of equations. The pressure-gradient system takes the form ρut + px = 0, ρυt + py = 0, ρEt + (up)x + (υp)y = 0. Here (u, υ) is the velocity, ρ is the density which is independent of time resulted from the splitting procedure, p is the pressure, and E = 1/2(u2 + υ2) + 1/γ-1 p/ρ is the energy. The natural (parabolically degenerate) boundary value is used.

Original languageEnglish (US)
Pages (from-to)1849-1868
Number of pages20
JournalCommunications in Partial Differential Equations
Volume22
Issue number11-12
DOIs
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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