| It is very important to study the generation and propagation of shock wave in fluid mechanics.Numerical simulation and physical experiments show that the structure of shock wave is very complex,which is determined by many factors,such as the density,velocity,pressure of fluid and geometry of obstacles.Mathematically,the rigorous theory of shock reflection is one of the difficult and hot issues in nonlinear partial differential equations.In this thesis,we will take nonlinear wave system and potential flow equation as examples to study the local theory of shock regular reflection for isothermal gas.The arrangement of this thesis is as follows.In the first chapter,the physical background and research status of shock reflection are introduced,and the structure of this thesis is given.In the second chapter,the nonlinear wave system for polytropic gas and isothermal gas are considered.Firstly,for the nonlinear wave system for polytropic gas,the existence and uniqueness of vertical reflection are proved when the wedge angle θw is π/2.According to the nonlinear wave system for isothermal gas,the critical condition for regular reflection of shock wave is derived.At this time,the wedge angle θw is allowed to be π/4<θw<π/2,which is a new physical phenomenon.In the third chapter,the potential flow equation for isothermal gas is considered.Firstly,the existence and uniqueness of shock reflection are proved when the wedge angle θw is equal to π/2.Then,considering the local existence of large angle wedge shock reflection for isothermal gas.The existence and uniqueness of the solution of the shock reflection problem is proved when θw is close to π/2. |
