By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, ...

A theoretical expression is developed for femtosecond coherent anti-Stokes Raman scattering (CARS) to quantitatively account for the vibrational line shape in the presence of nonresonant signal. The contributions of the resonant and nonresonant components are extracted from the emitted signal line shape as a function of Stokes wavelength and as a function of the temporal overlap of the two pump...

We present an analysis of the Navier–Stokes equations in framework algebraic approach to systems partial differential (the formal theory equations).

A large part of the modern theory of differential equations in the complex domain is concerned with regular singularities and holonomic systems. However the theory of differential equations with irregular singularities has a long history and has become very active in recent years. Substantial links of this theory to the theory of algebraic groups, commutative algebra, resurgent functions, and G...

We aim at justifying rigorously the low Mach number asymptotics for a model of compressible fluid coupled to the radiation. For simplicity, we restrict ourselves to the barotropic situation, and adopt the so-called P1-approximation to model the effects of radiation. We focus on small perturbations of stable constant equilibria. In the critical regularity framework, we establish estimates indepe...

We give a justification of the discrete analogue of Laplace’s method applied to the asymptotic estimation of sums consisting of positive terms. The case considered is the series related to the hypergeometric function pFq−1(x) (with q ≥ p + 1) as x → +∞ discussed by Stokes [Proc. Camb. Phil. Soc. 6 (1889) 362–366 ]. Two examples are given in which it is shown how higher order terms in the asympt...

advantages and disadvantages of using “stokes parameters” in exploration of inertia-gravity wave properties are discussed in this paper. the survey is carried out on an inertia-gravity wave event (igws in what follows) that occurred over iran from 7 to 9 february 2012. applying this technique for investigation of atmospheric igws was recommended by vincent and fritts (1987) and then developed b...

<p style='text-indent:20px;'>We prove the inviscid limit for incompressible Navier-Stokes equations data that are analytic only near boundary in a general two-dimensional bounded domain. Our proof is direct, using vorticity formulation with nonlocal condition, explicit semigroup of linear Stokes problem flatten boundary, and standard wellposedness theory Sobolev spaces away from boundary....

We present a theoretical and numerical study of horizontal particle dispersion due to random waves in the three-dimensional rotating and stratified Boussinesq system, which serves as a simple model to study the dispersion of tracers in the ocean by the internal wave field. Specifically, the effective one-particle diffusivity in the sense of Taylor (Proc. Lond. Math. Soc., vol. 20, 1921, p. 196)...