The proof of Proposition VI.4 on pages 487-489 in Section VI.3 should be modified as follows. VI.3. Estimates for |N |u e ||, 1 [ p < 2 We follow here closely the argument of [Bethuel-Brezis-He ´lein 2, Lemma X.13]. Let 1 [ p < 2 and set r=|u e |.
Asymptotics for the Ginzburg–Landau Equation in Arbitrary Dimensions
✍ Scribed by F Bethuel; H Brezis; G Orlandi
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 475 KB
- Volume
- 186
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
Let W be a bounded, simply connected, regular domain of R N , N \ 2. For 0 < e < 1, let u e : W Q C be a smooth solution of the Ginzburg-Landau equation in W with Dirichlet boundary condition g e , i.e.,
˛-Du
in W, u e =g e on "W.
📜 SIMILAR VOLUMES
In this paper, the authors have studied a generalized Ginzburg᎐Landau equation Ž . in two spatial dimensions 2D . They have shown that this equation, under periodic boundary conditions, has the maximal attractor with finite Hausdorff dimension. This rigorously establishes the foundation for further
## Abstract Spatially periodic equilibria __A__(__X, T__) = √1 − __q__^2^ __e__ are the locally preferred planform for the Ginzburg‐Landau equation ∂~__T__~__A__ = ∂^2^~__X__~__A__ + __A__ − __A__|__A__|^2^. To describe the global spatial behavior, an evolution equation for the local wave number __