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Well-posedness of the free surface problem on a Newtonian fluid between cylinders rotating at different speeds

Part of: Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  21 September 2021

Jiaqi Yang
Jiaqi Yang*
Affiliation:
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129, China (yjqmath@nwpu.edu.cn, yjqmath@163.com)
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Abstract

When a liquid fills the semi-infinite space between two concentric cylinders which rotate at different steady speeds, how about the shape of the free surface on top of the fluid? The different fluids will lead to a different shape. For the Newtonian fluid, the meniscus descends due to the centrifugal forces. However, for the certain non-Newtonian fluid, the meniscus climbs the internal cylinder. We want to explain the above phenomenon by a rigorous mathematical analysis theory. In the present paper, as the first step, we focus on the Newtonian fluid. This is a steady free boundary problem. We aim to establish the well-posedness of this problem. Furthermore, we prove the convergence of the formal perturbation series obtained by Joseph and Fosdick in Arch. Ration. Mech. Anal. 49 (1973), 321–380.

Keywords

Free boundary problemNewtonian fluidWell-posednessAsymptotic expansion

MSC classification

Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 35Q30: Navier-Stokes equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 5 , October 2022 , pp. 1251 - 1276
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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