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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)
Given any data points xx,...,x„ in R5 and values f(xx),... ,/(x„) of a function /, Shepard's global interpolation formula reads as follows: s°pf(x) = !/(*,>,(*). "*(*) -I* *,|"7D* xj\", ' j where | ■ | denotes the Euclidean norm in R*. This interpolation scheme is stable, but if p > 1, the gradient of the interpolating function vanishes in all data points.(More)
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital(More)
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 domain with compact boundary and nonzero Dirichlet boundary data. Recently, the first two authors of this article and F. Riechwald showed for an exterior domain the existence of Leray-Hopf type weak solutions. Starting from the proof of existence we will get a weak solution satisfying ‖v(t)‖2 → 0 as t → ∞ and(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)
Consider the Navier-Stokes system with initial value u 0 ∈ L 2 σ (Ω) and vanishing external force in a general (bounded or unbounded, smooth or nonsmooth) domain Ω ⊆ R 3 and a time interval [0, T), 0 < T ≤ ∞. Our aim is to characterize the largest possible space of initial values u 0 yielding a unique strong solution u in Serrin's class L 8 0, T ; L 4 (Ω).(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)