Two-Dimensional Model for otating Condensate

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 67)

Abstract

In this chapter, we want to study the shape of the minimizers u=uε H01D, C of
$$ E_\varepsilon (u) = \int_\mathcal{D} {\left\{ {\frac{1} {2}|\nabla u|^2 - \Omega r^ \bot \cdot (iu,\nabla u) + \frac{1} {{4_\varepsilon ^2 }}\left( {|u|^2 - \rho {\rm T}F(r)} \right)^2 } \right\} dxdy,} $$
(1)
Where r = (x, y), r = (−y, x), (iu,∇u)= i(ū∇u - (u∈ū)/2, ε is a small parameter, and Ω is the given rotational velocity. We assume that ρTF(r)= ρ0 −r2 D is the disc of radius R0= √ρ0 in R2 (so that ρTF = 0 on ∂D, and ∫D ρTF = 1, which prescribes the value of ρ0. The issue is to determine the number and location of vortices according to the value of Ω.

Keywords

Asymptotic Expansion Rotational Velocity Vortex Structure Critical Velocity Unique Positive Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Boston 2006

Personalised recommendations