\(L^q\) estimates of weak solutions to the stationary Stokes equations around a rotating body. (English) Zbl 1184.35241

The author establishes the existence, uniqueness and \(L^q\) estimates of weak solutions to the exterior problem for stationary Stokes equations which describe the fluid motion around a compact rigid body rotating with a prescribed constant angular velocity. The problem is difficult due to the presense of a drift term which cannot be trated as a simple perturbation. The mathematical tools are based on a dyadic decomposition, square function of Littlewood-Paley type, and a maximal function.


35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
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