A Nonlinear Degenerate Free-Boundary Problem and Subsonic-sonic flows

PDE Seminar
Thursday, November 19, 2009 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 255
Zhouping Xin – The Chinese University of Hong Kong
Zhiwu Lin
One of the challenges in the study of transonic flows is the understanding of the flow behavior near the sonic state due to the severe degeneracy of the governing equations. In this talk, I will discuss the well-posedness theory of a degenerate free boundary problem for a quasilinear second elliptic equation arising from studying steady subsonic-sonic irrotational compressible flows in a convergent nozzle. The flow speed is sonic at the free boundary where the potential flow equation becomes degenerate. Both existence and uniqueness will be shown and optimal regularity will be obtained. Smooth transonic flows in deLaval nozzles will also be discussed. This is a joint work with Chunpeng Wang.