Stokes Paradox, Fluid dynamics, Stokes flow, Stream function, Biharmonic equation, Helmholtz equation, Low Reynolds number This paper proposes a solution to Stokes’ paradox for asymptotically uniform viscous flow around a cylinder. The existence of a global stream function satisfying a perturbative form of the two-dimensional Navier–Stokes equations for low Reynolds number is established. This ...

We construct biharmonic real hypersurfaces and Lagrangian submanifolds of Clifford torus type in CPn via the Hopf fibration; and get new examples of biharmonic submanifolds in S as byproducts .

Let R be a Riemannian manifold without a biharmonic Green function defined on it and Ω a domain in R. A necessary and sufficient condition is given for the existence of a biharmonic Green function on Ω.

In this paper, we formulate a novel trivariate biharmonic B-spline defined over bounded volumetric domain. The properties of bi-Laplacian have been well investigated, but the straightforward generalization from bivariate case to trivariate one gives rise to unsatisfactory discretization, due to the dramatically uneven distribution of neighbouring knots in 3D. To ameliorate, our original idea is...

The concept of multilevel filtering (MF) preconditioning applied to second-order selfadjoint elliptic problems is briefly reviewed. It is then shown how to effectively apply this concept to other elliptic problems such as the second-order anisotropic problem, biharmonic equation, equations on locally refined grids and interface operators arising from domain decomposition methods. Numerical resu...

Optimizing eigenvalues of biharmonic equations appears in the frequency control based on density distribution of composite rods and thin plates with clamped or simply supported boundary conditions. In this paper, we use a rearrangement algorithm to find the optimal density distribution which minimizes a specific eigenvalue. We answer the open question regarding optimal density configurations to...

Martin COSTABEL & Monique DAUGE Abstract. The 2 2 system of integral equations corresponding to the biharmonic single layer potential in R2 is known to be strongly elliptic. It is also known to be positive definite on a space of functions orthogonal to polynomials of degree one. We study the question of its unique solvability without this orthogonality condition. To each curve , we associate a ...

In this paper, we consider the well known Morley nonconforming element approximation of a nonlinear biharmonic equation which is related to the well-known two-dimensional Navier–Stokes equations. Firstly, optimal energy and H1-norm estimates are obtained. Secondly, a two-level additive Schwarz method is presented for the discrete nonlinear algebraic system. It is shown that if the Reynolds numb...

In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds B and F into the doubly warped product f B ×b F can not be proper biharmonic maps. Also we analyze the conditions for the biharmonicity of projections f B ×b F → B and f B ×b F → F , respectively. Some characterizations for non-harmonic biharmonic maps are g...

For most `nice' elliptic boundary value problems there is a general expectation that the rst eigenfunction is unique and of xed sign. And indeed, for second order elliptic di erential equations with Dirichlet boundary conditions such a result holds as a consequence of the maximum principle. It is well known that such a maximum principle does not have a direct generalization to higher order elli...