Global subsonic and subsonic-sonic flows through infinitely long nozzles Chunjing XieZhouping Xin 35J2535J7035Q3576H05subsonic flowboundary gradient estimateHolder gradient estimatecomparision principlehodograph transformationcompensated compactnesssubsonic-sonic flow In this paper, we study global subsonic and subsonic-sonic flows through a general infinitely long nozzle. First, it is proved that there exists a critical value for the incoming mass flux so that a global uniformly subsonic flow exists in the nozzle as long as the incoming mass flux is less than the critical value. More importantly, we establish some uniform estimates for the deflection angles and the minimum speed of the subsonic flows by combining hodograph transformation and the comparison principle for elliptic equations. With the help of these properties and a compensated compactness framework, we get the existence of a global subsonic-sonic flow solution in the case of the critical incoming mass flux. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3108 10.1512/iumj.2007.56.3108 en Indiana Univ. Math. J. 56 (2007) 2991 - 3024 state-of-the-art mathematics http://iumj.org/access/