报告题目：Steady Euler Flows with Large Vorticity and Characteristic Discontinuities in Arbitrary Infinitely Long Nozzles
摘要：We establish the existence and uniqueness of compressible or incompressible Euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheet or entropy wave. We develop a new method to show the existence without assumptions of the sign of the second order derivatives on the velocity, or on the Bernoulli functions and the entropy functions at the inlet for the smooth case. Then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheet or Entropy wave by the compensated compactness. It is the first result on the global existence of solutions of the multi-dimensional steady compressible full Euler equations with free boundaries, which is not a perturbation of a piecewise constant solution. Finally, via the incompressible limit, we also establish the existence and uniqueness of incompressible Euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solution with vortex sheet. The methods and techniques developed in this paper may have applications in other related problems.