TY - JOUR

T1 - Scaling limits and regularity results for a class of Ginzburg-Landau systems

AU - Jerrard, Robert L.

AU - Soner, Halil Mete

N1 - Funding Information:
* Partially supported by the Army Research Office and the National Science Foundation through the Center for Nonlinear Analysis and by the NSF grant DMS-9200801. + Partially supported by the Army Research Office and the National Science Foundation through the Center for Nonlinear Analysis and by the NSF grants DMS-9200801, DMS-9500940, and by the AR0 grant DAAHO4-95-1-0226.

PY - 1999

Y1 - 1999

N2 - We study a class of parabolic systems which includes the Ginzburg-Landau heat flow equation, u∈t - Δu∈ + 1/∈2(|u∈|2 - 1)u∈ = 0 for u∈ : Rd → R2, as well as some natural quasilinear generalizations for functions taking values in Rk, k ≥ 2. We prove that for solutions of the general system, the limiting support as ∈ → 0 of the energy measure is a codimension k manifold which evolves via mean curvature. We also establish some local regularity results which hold uniformly in ∈. In particular, we establish a small-energy regulity theorem for the general system, and we prove a stronger regularity result for the usual Ginzburg-Landau equation on R2.

AB - We study a class of parabolic systems which includes the Ginzburg-Landau heat flow equation, u∈t - Δu∈ + 1/∈2(|u∈|2 - 1)u∈ = 0 for u∈ : Rd → R2, as well as some natural quasilinear generalizations for functions taking values in Rk, k ≥ 2. We prove that for solutions of the general system, the limiting support as ∈ → 0 of the energy measure is a codimension k manifold which evolves via mean curvature. We also establish some local regularity results which hold uniformly in ∈. In particular, we establish a small-energy regulity theorem for the general system, and we prove a stronger regularity result for the usual Ginzburg-Landau equation on R2.

UR - http://www.scopus.com/inward/record.url?scp=0013027307&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0013027307&partnerID=8YFLogxK

U2 - 10.1016/S0294-1449(99)80024-9

DO - 10.1016/S0294-1449(99)80024-9

M3 - Article

AN - SCOPUS:0013027307

VL - 16

SP - 423

EP - 466

JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

SN - 0294-1449

IS - 4

ER -