标题： 二阶抛物型方程组初边值问题的可解性带有三阶色散项 显示英文标题

标题： Solvability of an Initial-Boundary Value Problem for a Second Order Parabolic System with a Third Order Dispersion Term

摘要： 我们考虑一个带有三阶色散项的线性二阶抛物型方程组。 这种类型的系统在考虑描述浸入不可压缩和无粘流体中的轴向流动涡旋丝的非线性模型方程时会出现。 我们证明了抛物-色散方程组的初边值问题的可解性，该问题可以应用于涡旋丝的运动。 为此，我们提出了一种新的正则化技术，通过添加一个时空导数项。 显示英文摘要

摘要： 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 of 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.