A diffused interface whose chemical potential lies in a Sobolev space

Yoshihiro Tonegawa

Displaying similar documents to “A diffused interface whose chemical potential lies in a Sobolev space”

Vortex filament dynamics for Gross-Pitaevsky type equations

Robert L. Jerrard (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study solutions of the Gross-Pitaevsky equation and similar equations in $m \geq 3$ space dimensions in a certain scaling limit, with initial data $u_{0}^{ϵ}$ for which the jacobian $J u_{0}^{ϵ}$ concentrates around an (oriented) rectifiable $m - 2$ dimensional set, say $Γ_{0}$ , of finite measure. It is widely conjectured that under these conditions, the jacobian at later times $t > 0$ continues to concentrate around some codimension $2$ submanifold, say $Γ_{t}$ , and that the family ${Γ_{t}}$ of submanifolds evolves by binormal mean curvature flow....