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Asymptotic Analysis - Volume 77, issue 1-2

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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.

Quantum revivals in two degrees of freedom integrable systems: The torus case

Authors: Lablée, Olivier

Article Type: Research Article

Abstract: The paper deals with the semi-classical behaviour of quantum dynamics for a semi-classical completely integrable system with two degrees of freedom near Liouville regular torus. The phenomenon of wave packet revivals is demonstrated in this article. The framework of this paper is semi-classical analysis (limit: h→0). For the proofs we use standard tools of real analysis, Fourier analysis and basic analytic number theory.

Keywords: Schrödinger's dynamics, revivals of wave packets, semi-classical analysis of two degrees of freedom integrable systems

DOI: 10.3233/ASY-2011-1069

Citation: Asymptotic Analysis, vol. 77, no. 1-2, pp. 1-41, 2012

Price: EUR 27.50

Remarks on the large time behavior of viscosity solutions of quasi-monotone weakly coupled systems of Hamilton–Jacobi equations

Authors: Mitake, Hiroyoshi | Tran, Hung V.

Article Type: Research Article

Abstract: We investigate the large-time behavior of viscosity solutions of quasi-monotone weakly coupled systems of Hamilton–Jacobi equations on the n-dimensional torus. We establish a convergence result to asymptotic solutions as time goes to infinity under rather restricted assumptions.

Keywords: large-time behavior, Hamilton–Jacobi equations, weakly coupled systems, ergodic problem, viscosity solutions

DOI: 10.3233/ASY-2011-1071

Citation: Asymptotic Analysis, vol. 77, no. 1-2, pp. 43-70, 2012

Price: EUR 27.50

Remarks on the ill-posedness of the Prandtl equation

Authors: Gérard-Varet, D. | Nguyen, T.

Article Type: Research Article

Abstract: In the lines of the recent paper [J. Amer. Math. Soc. 23(2) (2010), 591–609], we establish various ill-posedness results for the Prandtl equation. By considering perturbations of stationary non-monotonic shear flows, we show that for some C∞ initial data, local in time H1 solutions of the linearized Prandtl equation do not exist. At the nonlinear level, we prove that if a flow exists in the Sobolev setting, it cannot be Lipschitz continuous. Besides ill-posedness in time, we also establish some ill-posedness in space, that casts some light on the results obtained by Oleinik for monotonic data.

Keywords: boundary layers, Prandtl equation, ill-posedness, temporal instability, spatial instability

DOI: 10.3233/ASY-2011-1075

Citation: Asymptotic Analysis, vol. 77, no. 1-2, pp. 71-88, 2012

Price: EUR 27.50

On the global existence for the axisymmetric Euler–Boussinesq system in critical Besov spaces

Authors: Sulaiman, Samira

Article Type: Research Article

Abstract: This paper is devoted to the global existence and uniqueness results for the three-dimensional Boussinesq system with axisymmetric initial data v0 ∈B5/2 2,1 (R3 ) and ρ0 ∈B1/2 2,1 (R3 )∩Lp (R3 ) with p>6. This system couples the incompressible Euler equations with a transport-diffusion equation governing the density. In this case the Beale–Kato–Majda criterion (see [2]) is not known to be valid and to circumvent this difficulty we use in a crucial way some geometric properties of the vorticity.

Keywords: axisymmetric flows, critical Besov spaces, global well-posedness

DOI: 10.3233/ASY-2011-1074

Citation: Asymptotic Analysis, vol. 77, no. 1-2, pp. 89-121, 2012

Price: EUR 27.50
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