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Contact discontinuities for 2-D inviscid compressible flows in infinitely long nozzles. (arXiv:1810.04411v1 [math.AP])
来源于:arXiv
We prove the existence of a subsonic weak solution $({\bf u}, \rho, p)$ to
steady Euler system in a two-dimensional infinitely long nozzle when
prescribing the value of the entropy $(= \frac{p}{\rho^{\gamma}})$ 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. 查看全文>>