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 Helmholtz decomposition and semigroup theory to the fluid around a moving body Bull. Korean Math. Soc.Published online November 7, 2019 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, semigroyp, fractional power of operator MSC numbers : 76D05, 35Q35 Full-Text :