Reinhard Farwig

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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)
We analyze in classical L(R)-spaces, n = 2 or n = 3, 1 < q < ∞, a singular integral operator arising from the linearization 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 Littlewood–(More)
Consider a smooth bounded domain Ω ⊆ R3, 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)
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 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)
S: On a phase-field model for two-phase flows of viscous incompressible fluids with degenerate mobility Helmut Abels University of Regensburg, Faculty for Mathematics 93040 Regensburg, Germany HELMUT.ABELS@MATHEMATIK.UNI-REGENSBURG.DE We discuss a recent model for the two-phase flow of two immiscible, incompressible fluids in the case when the densities of(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 system with initial value u0 ∈ Lσ(Ω) and vanishing external force in a general (bounded or unbounded, smooth or nonsmooth) domain Ω ⊆ R3 and a time interval [0, T ), 0 < T ≤ ∞. Our aim is to characterize the largest possible space of initial values u0 yielding a unique strong solution u in Serrin’s class L8 ( 0, T ;L4(Ω) ) . As(More)