The Existence And Stability Of Subsonic Flow In Infinitely Long Curved Pipes

In this paper,a flow through a nozzle can be considered as a steady,isentropic,irrotational flow,so we are concerned with the existence and stability of a subsonic global solution in an infinitely long curved nozzle for the steady potential flow equation.By using Bernoulli's law and implicit function theorem,we transform this problem into a problem for solving second-order quasilinear partial differential equation.During the research process,some suitably weighted H(?)lder spaces will be introduced.At the same time,by establishing a series of a priori estimates on the solution to second order linear elliptic equation in an unbounded strip domain with two Neumann boundary conditions and one periodic boundary condition with respect to some variable,we show the global existence and stability of the soiution of potential flow equation in a nozzle when the state of subsonic flow at negative infinity is given.Furthermore,we also study the asymptotic state of the subsonic solution at positive infinity as well as the asymptotic behavior at minus infinity.This article is organized as follows:The first chapter introduces the research background and significance of the subsonic flow problem,it briefly expounds the research status of the subject and establishes the basic direction and main content of this paper.The second chapter considers the subsonic flow described by the potential flow equation in a two-dimensional infinitely long curved nozzle.The expected results and related conclusions are given and proved.The third chapter first introduces the expected results and main conclusions of the subsonic flow in the three-dimensional infinitely long curved nozzle and defines the anisotropic weighted H(?)lder space.Then we study the solvability and prior estimates for the linearization problem.Essentially we need to analyze and establish a priori estimates of the Poisson equation ?u=(?)(z) in the strip domain(?).By using the separation variable method,we can derive the formal expression of u(z) in(?).Subsequently,Thus we can further obtain the existence and regularity of u(z) in(?).Finally,the proof of the main theorem of this paper is expounded.We define the suitably function space and use the contraction mapping principle to show the existence and uniqueness of global subsonic flow in 3D nozzle.Based on the crucial estimates and properties given in the third chapter,by use of the standard nonlinear iteration scheme,we can complete the proof of the main theorem and further obtain the asymptotic behavior of ?_x? negative and positive infinity in the strip domainWrespectively.