Solvability of an initial-boundary value problem for a second order parabolic system with a third order dispersion term

Masashi Aiki, Tatsuo Iguchi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider a linear second order parabolic system with a third order dispersion term. This type of system arises when considering a nonlinear model equation describing the motion of a vortex filament with axial flow immersed in an incompressible and inviscid fluid. We prove the solvability of an initial-boundary value problem for the parabolic-dispersive system which allows application to the motion of a vortex filament. To do so, we propose a new regularization technique by adding a space-time derivative term.

Original languageEnglish
Pages (from-to)3388-3411
Number of pages24
JournalSIAM Journal on Mathematical Analysis
Volume44
Issue number5
DOIs
Publication statusPublished - 2012

Fingerprint

Vortex Filament
Second-order Systems
Parabolic Systems
Initial-boundary-value Problem
Boundary value problems
Solvability
Vortex flow
Regularization Technique
Motion
Axial flow
Linear Order
Term
Nonlinear Model
Space-time
Derivatives
Fluid
Derivative
Fluids

Keywords

  • Initial-boundary value problem
  • Parabolic regularization
  • Parabolic-dispersive system
  • Vortex filament

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

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AB - We consider a linear second order parabolic system with a third order dispersion term. This type of system arises when considering a nonlinear model equation describing the motion of a vortex filament with axial flow immersed in an incompressible and inviscid fluid. We prove the solvability of an initial-boundary value problem for the parabolic-dispersive system which allows application to the motion of a vortex filament. To do so, we propose a new regularization technique by adding a space-time derivative term.

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