Asymptotic Analysis - Volume 42, issue 3-4

Authors: Charve, Frédéric

Article Type: Research Article

Abstract: On s'intéresse ici au comportement des solutions faibles de Leray du système primitif lorsque le nombre de Rossby tend vers zéro. On sépare notamment la solution en deux parties chacune solution d'un système particulier, l'une appelée partie oscillante, l'autre partie quasigéostrophique. La première tend vers zéro lorsque la rotation devient forte et de la seconde on peut extraire une sous‐suite tendant vers une solution du système quasigéostrophique.

Keywords: système primitif, système quasigéostrophique, anisotropie, inégalités de Strichartz, primitive system, quasigeostrophic system, anisotropy, Strichartz inequalities

Citation: Asymptotic Analysis, vol. 42, no. 3-4, pp. 173-209, 2005

Authors: Texier, Benjamin

Article Type: Research Article

Abstract: The Euler–Maxwell system of equations is a complex, hydrodynamical model for the description of laser–plasma interactions. We introduce non‐dimensional variables, exhibit a small parameter ε and study various WKB approximations with respect to ε for this system, under a polarization condition for the initial data. We justify an approximation by a weak Zakharov equation for times O(1) and an approximation by a Davey–Stewartson equation for times O(|log ε|). Our key observation is that the Euler–Maxwell exhibit transparency properties, similar to the properties exhibited by Joly, Métivier and Rauch for Maxwell–Bloch systems. These properties imply in particular that in a weakly nonlinear …regime, the geometric optics approximation is given by a linear equation. Show more

Citation: Asymptotic Analysis, vol. 42, no. 3-4, pp. 211-250, 2005

Authors: Laurençot, Philippe

Article Type: Research Article

Abstract: Convergence of integrable and bounded entropy solutions to a simplified model for radiating gases towards the source‐type solution to the viscous Burgers equation is shown by a rescaling method. Temporal decay estimates for zero‐mass solutions are also established.

Keywords: temporal decay estimates, rescaling method, viscous Burgers equation

Citation: Asymptotic Analysis, vol. 42, no. 3-4, pp. 251-262, 2005

Authors: DeVille, R.E. Lee | Wayne, C. Eugene

Article Type: Research Article

Abstract: In this paper, we consider a scalar wave equation on a thin, laminated, three‐dimensional plate. We show that if the plate is sufficiently thin, then there is a hierarchy of two‐dimensional equations whose dynamics model the dynamics of the full plate, each of which successively lengthens the time interval over which the approximation holds.

Citation: Asymptotic Analysis, vol. 42, no. 3-4, pp. 263-309, 2005

Authors: DeVille, R.E. Lee

Article Type: Research Article

Abstract: In a companion paper, we considered a scalar wave equation on a thin, laminated, three‐dimensional plate. We showed that if the plate was sufficiently thin, then there exists a hierarchy of two‐dimensional equations whose dynamics model the dynamics of the full plate, each of which successively lengthens the time interval over which the approximation is valid. In certain cases, these approximating equations may formally be ill‐posed. In this paper, we consider modifications of the approximating equations which are themselves well‐posed, and which qualitatively afford the same approximation. We also present an algorithm to compute the coefficients in the approximating equations …in closed form, and show numerical evidence that the estimates on the efficacy of the approximating equations are sharp. Show more

Citation: Asymptotic Analysis, vol. 42, no. 3-4, pp. 311-346, 2005

Article Type: Other

Citation: Asymptotic Analysis, vol. 42, no. 3-4, pp. 347-347, 2005