Maximal regularity for the Stokes system on noncylindrical space-time domains (Q2501652)

The author establishes \(L^p\)-\(L^q\) maximal regularity estimates for the Stokes equations in spatial regions with moving boundary, including bounded and unbounded regions. The problem is reduced to an equivalent abstract nonautonomous Cauchy problem in a cylindrical space-time domain. Then a refined theory of boundedly invertible operators in Banach spaces allows to obtain the desired regularity. The results are applied to the Stokes equations in three-dimensional domains rotating around a fixed axis.