Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2020; 57(3): 661-676

Online first article November 7, 2019      Printed May 31, 2020

https://doi.org/10.4134/BKMS.b190403

Copyright © The Korean Mathematical Society.

Helmholtz decomposition and semigroup theory to the fluid around a moving body

Hyeong-Ohk Bae

Ajou University

Abstract

To understand the interaction of a fluid and a rigid body, we use the concept of $B$-evolution. Then in a similar way to the usual Navier-Stokes system, we obtain a Helmholtz type decomposition. Using $B$-evolution theory and the decomposition, we work on the semigroup to analyze the linear part of the system.

Keywords: Helmholtz decomposition, fluid, rigid body, $B$-evolution, semigroup, fractional power of operator

MSC numbers: 76D05, 35Q35

Supported by: This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2015R1 D1A1A01057976, 2018R1D1A1A09082848).