TY - JOUR
T1 - Solvability of an initial-boundary value problem for a second order parabolic system with a third order dispersion term
AU - Aiki, Masashi
AU - Iguchi, Tatsuo
PY - 2012
Y1 - 2012
N2 - 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.
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.
KW - Initial-boundary value problem
KW - Parabolic regularization
KW - Parabolic-dispersive system
KW - Vortex filament
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U2 - 10.1137/120861163
DO - 10.1137/120861163
M3 - Article
AN - SCOPUS:84868348837
SN - 0036-1410
VL - 44
SP - 3388
EP - 3411
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 5
ER -