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\(L^q\)-theory of a singular ”winding” integral operator arising from fluid dynamics. (English) Zbl 1057.35028
The authors study the solvability of a system of partial differential equations of second order involving an angular derivative which is not subordinate to the Laplacian. This system arises from the linearization of the Navier-Stokes equations of a three-dimensional rigid body rotating in a viscous incompressible fluid. The solvability in \(L^q({\mathbb R}^n)\) is obtained by means of studying the properties of the singular operator arising from the fundamental solution.

MSC:
35Q30 Navier-Stokes equations
76U05 General theory of rotating fluids
35B45 A priori estimates in context of PDEs
47G10 Integral operators
76D05 Navier-Stokes equations for incompressible viscous fluids
42B25 Maximal functions, Littlewood-Paley theory
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