Steady Subsonic Ideal Flows Through an Infinitely Long Nozzle with Large Vorticity
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In this paper, the existence, uniqueness, and far field behavior of a class of subsonic flows with large vorticity for the steady Euler equations in infinitely long nozzles are established. More precisely, for any given convex horizontal velocity of incoming flow in the upstream, there exists a critical value mcr, if the mass flux is larger than mcr, then there exists a unique smooth subsonic Euler flow through the infinitely long nozzle. This well-posedness result is proved by a new observation for the method developed in Xie and Xin (SIAM J Math Anal 42:751–784, 2010) to deal with the Euler system. Furthermore, the optimal convergence rates of the subsonic flows at far fields are obtained via the maximum principle and an elaborate choice of the comparison functions.
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