Strong 𝐿^{𝑝}-solutions to the Navier-Stokes flow past moving obstacles: The case of several obstacles and time dependent velocity

Abstract

Consider the Navier-Stokes flow past several moving or rotating obstacles with possible time-dependent velocity. It is shown that under suitable assumptions on the data, there exists a unique, local strong solution in the L p − L q L^p-L^q -setting for suitable p , q ∈ ( 1 , ∞ ) p,q \in (1,\infty ) . Moreover, it is proved that this strong solution coincides with the known mild solution in the very weak sense.