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\(L^p\)-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle. (English) Zbl 1102.76015
Summary: We consider the Navier-Stokes equations in the exterior of a rotating domain. It is shown that, after rewriting the problem in a fixed domain \(\Omega\), the solution of the corresponding Stokes equation is governed by a \(C_0\)-semigroup on \(L_\sigma^p(\Omega)\), \(1<p<\infty\), with generator \(Au= P(\Delta u+Mx\cdot\nabla u-Mu)\) . Moreover, for \(p\geq n\) and initial data \(u_0\in L_\sigma^p(\Omega)\), we prove the existence of a unique local mild solution to the Navier-Stokes problem.

MSC:
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
35B65 Smoothness and regularity of solutions to PDEs
44A10 Laplace transform
76U05 General theory of rotating fluids
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