A series of innovative and high-level achievements have been made in these fields, especially several open problems in the mathematical theory of fluid dynamics have been solved in cooperation with others, such as: (1) cone shock wave for compressible fluid, which proves the global existence and stability of supersonic shock wave and transonic shock wave solutions; (2) The phenomenon of transonic flow and transonic shock wave in the pipeline is an important basic problem in the theory of aerodynamic mathematics. For the Delaval pipeline in the wind tunnel experiment, if the outlet pressure is appropriately large, a stable transonic shock wave will be formed when the supersonic flow passes through the narrow mouth and reaches the wide mouth. However, the strict mathematical proof of this problem has always been an unsolved conjecture, and Professor Yin Huicheng and his collaborators have basically solved this problem. The related research results have been published in the international first-class mathematical magazines (comm.pureappl.math, comm.math.phys, arch. Rat.Mech.Anal, Math.Z, J.D.E, Pacific J.Math, etc. ), and was quoted and praised by some famous mathematicians, such as Mor, a member of the American Academy of Sciences.
Among them, the paper published in Comm.Math.Phys was listed as the landmark achievement of the last major national project (973 Core Mathematics).