Reinhard Farwig

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We analyze in classical L q (R n)-spaces, n = 2 or n = 3, 1 < q < ∞, a singular integral operator arising from the lin-earization of a hydrodynamical problem with a rotating obstacle. The corresponding system of partial differential equations of second order involves an angular derivative which is not subordinate to the Laplacian. The main tools are(More)
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The goal of this short course is to review the basic ingredients of the analysis and discretization of saddlepoint systems that arise in the weak formulation of fluid flow problems. As one model problem, we consider the slow and steady flow of a viscous incompressible fluid in some bounded domain governed by the Stokes equations −ν∆u + ∇p = f , in Ω, divu =(More)
Consider the Navier-Stokes equations in a smooth bounded domain Ω ⊂ R 3 and a time interval [0, T), 0 < T ≤ ∞. It is well-known that there exists at least one global weak solution u with vanishing boundary values u ∂Ω = 0 for any given initial value u 0 ∈ L 2 σ (Ω), external force f = div F , F ∈ L 2 0, T ; L 2 (Ω) , and satisfying the strong energy(More)
Title: The fundamental solution of compressible and incompressible fluid flow past a rotating obstacle Abstract: We consider the flow of either an incompressible or a compressible fluid around or past a rotating rigid body in the whole space R 3. Using a global coordinate transform and a linearization the problem reduces to a linear PDE system in a(More)
Consider a smooth bounded domain Ω ⊆ R 3 , a time interval [0, T), 0 < T ≤ ∞, and a weak solution u of the Navier-Stokes system. Our aim is to develop several new sufficient conditions on u yielding uniqueness and/or regularity. Based on semigroup properties of the Stokes operator we obtain that the local left-hand Serrin condition for each t ∈ (0, T) is(More)
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