Year: 2024
Type: preprint
Abstract: This paper is concerned with self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the flux to guarantee the existence of self-similar solutions of a given type. We also investigate the uniqueness and non-uniqueness of flows with a given type, which not only give rigorous justifications for some statements in \cite{Rosenhead40} but also show that some numerical computations in \cite{Rosenhead40} may not be precise. The non-uniqueness result is a new phenomenon for these flows. As a consequence of the classification of self-similar solutions in the half-space, we characterize the leading order term of the steady Navier-Stokes system in an aperture domain when the flux is small. The main approach is to study the ODE system governing self-similar solutions, where the detailed properties of both complete and incomplete elliptic functions have been investigated.
Source: arXiv (Cornell University)
Authors: Bang, Jeaheang, Gui, Changfeng, Liu, Hao, Wang, Yun, Xie, Chunjing
Institutions: Soochow University, Shanghai Jiao Tong University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: United Mitochondrial Disease Foundation, National Natural Science Foundation of China, Government of Jiangsu Province, Natural Science Foundation of Jiangsu Province, Universidade de Macau, Fundo para o Desenvolvimento das Ciências e da Tecnologia, Fundamental Research Funds for the Central Universities, Program of Shanghai Academic Research Leader
OpenAlex ID: W4405255155