雷诺边界下解的存在性与唯一性研究

Reynolds boundary condition is a boundary condition for the solution of the Reynolds equation under rich oil. For engineering application, Reynolds boundary condition means that the whole calculation domain is divided into oil existence domain and the cavitation domain. This division will be adjusted by the pressure condition in the calculation to satisfy the natural boundary conditions. On the other hand, the oil film pressure can also be obtained according to the hypothetical partition of the oil existence domain and the cavitation domain. The relationship between the Reynolds boundary condition and the hypothetical partition is established. The existence and uniqueness of the solution under the Reynolds boundary condition are analyzed via this relationship. If all pressure is non negative according to a hypothetical partition, this hypothetical partition is called legal. The following conjecture is given: the oil existence region in the solution of the Reynolds equation under the Reynolds boundary condition is the union of the existence regions of oil film in all legal hypothetical partition. The solution of Reynolds equation in one dimension is analyzed. In this paper, the uniqueness and existence of solutions for one and two dimensional discrete Reynolds equations are analyzed. The research content of this paper has been relatively complete in the engineering sense, but it still needs to be further improved in the mathematical sense