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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics