You are viewing a javascript disabled version of the site. Please enable Javascript for this site to function properly.
Go to headerGo to navigationGo to searchGo to contentsGo to footer
In content section. Select this link to jump to navigation

Asymptotic Analysis - Volume 104, issue 3-4

Purchase individual online access for 1 year to this journal.

Price: EUR 420.00
ISSN 0921-7134 (P)
ISSN 1875-8576 (E)

Impact Factor 2024: 1.1

The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. 

Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.

Elliptic estimates for the Dirichlet–Neumann operator on a corner domain

Authors: Ming, Mei | Wang, Chao

Article Type: Research Article

Abstract: We consider the elliptic estimates for the Dirichlet–Neumann operator related to the water waves problem on a two-dimensional corner domain in this paper. Due to the singularity of the boundary, there will be singular parts in the solution of the elliptic problem for the D–N operator. To begin with, we study elliptic problems with mixed boundary conditions to derive singularity decompositions and estimates. Based on this analysis, we present the estimates for both the D–N operator and its shape derivative with the existence of singular parts.

Keywords: Elliptic estimate, Dirichlet–Neumann operator, corner domains, water waves problem

DOI: 10.3233/ASY-171427

Citation: Asymptotic Analysis, vol. 104, no. 3-4, pp. 103-166, 2017

Price: EUR 27.50

Asymptotic expansion in Gevrey spaces for solutions of Navier–Stokes equations

Authors: Hoang, Luan T. | Martinez, Vincent R.

Article Type: Research Article

Abstract: In this paper, we study the asymptotic behavior of solutions to the three-dimensional incompressible Navier–Stokes equations (NSE) with periodic boundary conditions and potential body forces. In particular, we prove that the Foias–Saut asymptotic expansion for the regular solutions of the NSE in fact holds in all Gevrey classes . This strengthens the previous result obtained in Sobolev spaces by Foias–Saut. By using the Gevrey-norm technique of Foias–Temam, the proof of our improved result simplifies the original argument of Foias–Saut, thereby, increasing its adaptability to other dissipative systems. Moreover, the expansion is extended to all Leray–Hopf weak solutions.

Keywords: 3D Navier–Stokes equations, Leray–Hopf weak solutions, asymptotic expansions, eventual regularity, Gevrey class

DOI: 10.3233/ASY-171429

Citation: Asymptotic Analysis, vol. 104, no. 3-4, pp. 167-190, 2017

Price: EUR 27.50

Existence and stability of the steady state solution of a thin film on an inclined periodic solid substrate under gravity

Authors: Alhasanat, Ahmad | Ou, Chunhua

Article Type: Research Article

Abstract: In this paper, we investigate the dynamics of a liquid film flowing over a periodic wavy wall. This study is based on a long-wave model that is valid at near-critical Reynolds number. For the periodic wall surface, we prove the existence of a periodic steady-state solution to the model by the method of abstract contraction mapping in a particular functional space. Using the Floquet–Bloch theory and asymptotic method, we establish several analytic results on the stability of the periodic steady-state solution in a weighted functional space.

Keywords: Thin film flow, periodic solution, asymptotic analysis

DOI: 10.3233/ASY-171431

Citation: Asymptotic Analysis, vol. 104, no. 3-4, pp. 191-207, 2017

Price: EUR 27.50

Author Index Volume 104 (2017)

Article Type: Other

Citation: Asymptotic Analysis, vol. 104, no. 3-4, pp. 209-209, 2017

Get PDF
Show more