SELF-SIMILAR SOLUTIONS TO THE STEADY NAVIER-STOKES EQUATIONS IN A TWO-DIMENSIONAL SECTOR

作     者：Bang, Jeaheang Gui, Changfeng Liu, Hao Wang, Yun Xie, Chunjing 

作者机构：Institute for Theoretical Sciences Westlake University China Department of Mathematics Faculty of Science and Technology University of Macau Taipa China School of Mathematical Sciences Institute of Natural Sciences Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China School of Mathematical Sciences Center for dynamical systems and differential equations Soochow University Suzhou China School of Mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing CMA-Shanghai Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Navier Stokes equations 

摘      要：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 of the flow 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. The non-uniqueness result is a new phenomenon for these flows. Our results not only give rigorous justifications for some statements in [23] but also show that some numerical computations in [23] may not be precise. 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. Copyright © 2024, The Authors. All rights reserved.