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.
Received April 16, 2019; Revised July 22, 2019; Accepted September 25, 2019. 2010 Mathematics Subject Classification. 76D05, 35Q35. Key words and phrases. Helmholtz decomposition, fluid, rigid body, B-evolution, semigroup, fractional power of operator. 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).
