Boundary integral numerical methods are among the most accurate for interfacial Stokes flow, and widely applied. They have advantage that only boundary of domain must be discretized, which reduces number discretization points allows treatment complicated interfaces. Despite their popularity, there is no analysis convergence these flow. In practice, stability discretizations formulation can depe...

Abstract In this paper, we study the fractional nonlinear Rayleigh–Stokes equation under nonlocal integral conditions, and existence uniqueness of mild solution to our problem are considered. The ill-posedness recovering initial value is also investigated. To tackle ill-posedness, a regularized constructed by Fourier truncation method, convergence rate exact method demonstrated.

the earth’s gravity field dedicated missions, champ, grace and goce have opened up a new era for the study of the earth’s gravity field. the missions measure different functionals on the earth’s gravitational potential which are represented in terms of the stokes coefficients or the so-called geopotential models. the mapping process of the observations into the coefficients is called recovery o...

Abstract—In this work, we use the numerical steepest descent path (numerical SDP) method in complex analysis theory to calculate the highly oscillatory physical optics (PO) integral with quadratic phase and amplitude variations on the triangular patch. The Stokes’ phenomenon will occur due to various asymptotic behaviors on different domains. The stationary phase point contributions are careful...

We study the motion of a ferromagnetic helical nanostructure under the action of a rotating magnetic field. A variety of dynamical configurations were observed that depended strongly on the direction of magnetization and the geometrical parameters, which were also confirmed by a theoretical model, based on the dynamics of a rigid body under Stokes flow. Although motion at low Reynolds numbers i...

We study the condition number of the system matrices that appear in the Boundary Element Method when solving the Stokes equations at a two-dimensional domain. At the boundary of the domain we impose Dirichlet conditions or mixed conditions. We show that for certain critical boundary contours the underlying boundary integral equation is not solvable. As a consequence, the condition number of the...

1 2 Contents 0. One-variable calculus 1. The derivative 2. Inverse function and implicit function theorem 3. Fundamental local existence theorem for ODE 4. The Riemann integral in n variables 5. Integration on surfaces 6. Differential forms 7. Products and exterior derivatives of forms 8. The general Stokes formula 9. The classical Gauss, Green, and Stokes formulas 10. Holomorphic functions and...