Existence and Uniqueness of Reynolds equation under natural boundary conditions
Abstract
For the problem of solving Reynolds equation under natural boundary conditions, the corresponding hypothetical solution can be obtained by assuming the free boundary. If the solution satisfies natural boundary conditions, then the boundary is the boundary we are looking for. Obviously, there is a set S formed by all the boundaries that assume the solution is positive. We prove equivalence between maximum element of S and natural condition. We prove the closeness of set S under addition. Therefore, we prove that the set S must have a unique greatest element. Furthermore, we obtain the uniqueness and existence of solutions of Reynolds equation under natural boundary conditions. In engineering, the zero setting method is often used to find the boundary of Reynolds equation, and we also give the proof that the zero setting method has only one iterative error solution. We give an algorithm for solving Reynolds equation under one-dimensional conditions, which reaches the theoretical upper bound. We discuss the physical meaning of this method at the end.
Keywords
Cite
@article{arxiv.2211.10632,
title = {Existence and Uniqueness of Reynolds equation under natural boundary conditions},
author = {Wang Qun},
journal= {arXiv preprint arXiv:2211.10632},
year = {2022}
}
Comments
I hope to officially publish this article. Editors and other researchers who want to cooperate can contact me through my email [email protected]