Asymptotic Analysis - Volume 49, issue 1-2

Authors: Miura, Hideyuki | Sawada, Okihiro

Article Type: Research Article

Abstract: Koch and Tataru (Adv. Math. 157 (2001), 22–35) showed that the Cauchy problem of the Navier–Stokes equations has a time-local mild solution, when the initial velocity a∈vmo−1 (or, a∈bmo−1 and ‖a‖bmo−1 is small enough). The purpose of this paper is to estimate the regularizing rates for the higher-order derivatives of the mild solution. As an application of these estimates, it is proved that the solution is analytic in space variables. Moreover, it is also shown that the Serrin's condition leads to the spatial analyticity of the solution.

Keywords: Navier–Stokes equations, Koch–Tataru's solution, regularizing rate, spatial analyticity

Citation: Asymptotic Analysis, vol. 49, no. 1-2, pp. 1-15, 2006

Authors: Karali, Georgia

Article Type: Research Article

Abstract: We consider a finite number of particles initially close to spherical but of varying size exhibiting the property of preserving the measure of each connected component. We show that under the assumptions (i) particle size/interparticle distance «1 and (ii) initial deviation from sphericity/particle size «1 the particles retain their almost spherical shape and the dynamics of the system is determined by the motion of the centers. This is in sharp contrast with the Mullins–Sekerka free boundary problem where the particle centers remain almost fixed and the dynamics of the system is determined by the evolution of the radii.

Citation: Asymptotic Analysis, vol. 49, no. 1-2, pp. 17-37, 2006

Authors: Cherednichenko, Kirill D.

Article Type: Research Article

Abstract: The problem of periodic homogenisation for a conducting two-phase composite exhibiting non-locality in the overall behaviour is considered. The matrix is isotropic and its conductivity is constant, while the fibre-shaped inclusions are assumed to be anisotropic, with high contrast between conductivities along the fibres and in the transverse directions. The contrast is set to correspond to the so-called double-porosity scaling, which is of special interest. A full two-scale asymptotic expansion for the solution is constructed and rigorously justified via appropriate error estimates. An example of the non-local homogenised operator in the case of fibres with circular cross-sections is given.

Keywords: composite materials, homogenisation, non-local effects, asymptotic expansions

Citation: Asymptotic Analysis, vol. 49, no. 1-2, pp. 39-59, 2006

Authors: Vodev, Georgi

Article Type: Research Article

Abstract: We prove dispersive estimates for solutions to the Schrödinger equation with a real-valued potential V∈L∞ (Rn ), n≥4, satisfying V(x)=O(〈x〉−(n+2)/2−ε ), ε>0.

Citation: Asymptotic Analysis, vol. 49, no. 1-2, pp. 61-86, 2006

Authors: Amstutz, Samuel

Article Type: Research Article

Abstract: In the present work, the notion of topological sensitivity is extended to the case of a local perturbation of the properties of the material constitutive of the domain. As a model example, we consider the problem −div(αε A∇uε )+βε uε =Fε in two and three dimensions, where A is a symmetric positive definite matrix and αε ,βε ,Fε are functions whose values inside a small subdomain ωε are different from those of the background medium. An adjoint method is used to determine an asymptotic expansion of a given criterion when the diameter of ωε goes to …zero. Show more

Keywords: topology optimization, topological sensitivity analysis, detection of inclusions

Citation: Asymptotic Analysis, vol. 49, no. 1-2, pp. 87-108, 2006

Authors: Sueur, Franck

Article Type: Research Article

Abstract: We consider the Euler system of compressible and entropic gaz dynamics in a bounded open domain of $\mathbb {R}$ d with wall boundary condition. We prove the existence and the stability of families of solutions which correspond to a ground state plus a large entropy boundary layer. The ground state is a solution of the Euler system which satisfies some explicit additional conditions on the boundary. These conditions are used in a reduction of the system. We construct BKW expansions at all order. The profile problems are linear thanks to a transparency property. We prove the stability of …these expansions by proving ε-conormal estimates for a characteristic boundary value problem. Show more

Citation: Asymptotic Analysis, vol. 49, no. 1-2, pp. 109-171, 2006