We obtain some classification results and the stability conditions of nonminimal biharmonic anti-invariant submanifolds in Sasakian space forms. MSC 2000: 53C42 (primary); 53B25 (secondary)

This paper is concerned with the accurate numerical approximation of the spectral properties of the biharmonic operator on various domains in two dimensions. A number of analytic results concerning the eigenfunctions of this operator are summarized and their implications for numerical approximation are discussed. In particular, the asymptotic behaviour of the first eigenfunction is studied sinc...

We consider the nonlinear biharmonic Schr\"odinger equation $$i\partial_tu+(\Delta^2+\mu\Delta)u+f(u)=0,\qquad (\text{BNLS})$$ in critical Sobolev space $H^s(\R^N)$, where $N\ge1$, $\mu=0$ or $-1$, $0<s<\min\{\fc N2,8\}$ and $f(u)$ is a function that behaves like $\lambda\left|u\right|^{\alpha}u$ with $\lambda\in\mathbb{C},\alpha=\frac{8}{N-2s}$. prove existence uniqueness of global solutions t...

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 explore an application of the Physics-Informed Neural Networks (PINNs) in conjunction with Airy stress functions and Fourier series to find optimal solutions a few reference biharmonic problems elasticity elastic plate theory. Biharmonic relations are fourth-order partial differential equations (PDEs) that challenging solve using classical numerical methods have not been addressed PINNs. Our...

Dual conservation laws of linear planar elasticity theory have been systematically studied based on stress function formalism. By employing generalized symmetry transformation or Lie–B€acklund transformation, a class of new dual conservation laws in planar elasticity have been discovered based on Noether theorem and its Bessel–Hagen generalization. These dual conservation laws represent variati...

An analogue technique for the approximate solution of the biharmonic equation is used to determine the viscous drag at Reynolds number approaching zero for cylinders falling symmetrically in a liquid between parallel walls. Results obtained show good agreement with numerical solutions, with results by direct experiment and with the work of other authors. Streamlines are obtained with a maximum ...