For any critical point of the complex Ginzburg-Landau functional in dimension 3, we prove that, for large coupling constants, κ = 1/ε; if the energy of this critical point on a ball of a given radius r is relatively small compared to r log r/ε, then the ball of half-radius contains no vortex (the modulus of the solution is larger than 1/2). We then show how this property can be applied to describe limiting vortices as ε → 0.
|Original language||English (US)|
|Number of pages||23|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - Feb 1 2001|
ASJC Scopus subject areas
- Applied Mathematics