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).