14 citations · 51 across the 12 of their papers we have counts for
15 papers
The nonlinear shallow water equations with a partially immersed obstacle
David Lannes, Tatsuo Iguchi
This article is devoted to the proof of the well-posedness of a model describing waves propagating in shallow water in horizontal dimension and in the presence of a fixed par…
A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part II: Justification as a shallow water approximation
Vincent Duchêne, Tatsuo Iguchi
We consider the Kakinuma model for the motion of interfacial gravity waves. The Kakinuma model is a system of Euler-Lagrange equations for an approximate Lagrangian, which is obtai…
A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part I: Structures and well-posedness
Vincent Duchêne, Tatsuo Iguchi
We consider a model, which we named the Kakinuma model, for interfacial gravity waves. As is well-known, the full model for interfacial gravity waves has a variational structure wh…
Solitary wave solutions to the Isobe-Kakinuma model for water waves
Mathieu Colin, Tatsuo Iguchi
We consider the Isobe-Kakinuma model for two-dimensional water waves in the case of the flat bottom. The Isobe-Kakinuma model is a system of Euler-Lagrange equations for a Lagrangi…
A Hamiltonian structure of the Isobe-Kakinuma model for water waves
Vincent Duchêne, Tatsuo Iguchi
We consider the Isobe-Kakinuma model for water waves, which is obtained as the system of Euler-Lagrange equations for a Lagrangian approximating Luke's Lagrangian for water waves.…
Hyperbolic free boundary problems and applications to wave-structure interactions
Tatsuo Iguchi, David Lannes
Motivated by a new kind of initial boundary value problem (IBVP) with a free boundary arising in wave-structure interaction, we propose here a general approach to one-dimensional I…
A mathematical justification of the Isobe-Kakinuma model for water waves with and without bottom topography
Tatsuo Iguchi
We consider the Isobe-Kakinuma model for water waves in both cases of the flat and the variable bottoms. The Isobe-Kakinuma model is a system of Euler-Lagrange equations for an app…
Solvability of the initial value problem to the Isobe-Kakinuma model for water waves
Ryo Nemoto, Tatsuo Iguchi
We consider the initial value problem to the Isobe-Kakinuma model for water waves and the structure of the model. The Isobe-Kakinuma model is the Euler-Lagrange equations for an ap…
Isobe-Kakinuma model for water waves as a higher order shallow water approximation
Tatsuo Iguchi
We justify rigorously an Isobe-Kakinuma model for water waves as a higher order shallow water approximation in the case of a flat bottom. It is known that the full water wave equat…
Motion of a Vortex Filament in an External Flow
Masashi Aiki, Tatsuo Iguchi
We consider a nonlinear model equation describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. In the present problem setting, we also take int…
A Mathematical Justification of a Thin Film Approximation for the Flow down an Inclined Plane
Hiroki Ueno, Tatsuo Iguchi
We consider a two-dimensional motion of a thin film flowing down an inclined plane under the influence of the gravity and the surface tension. In order to investigate the stability…
Uniform Estimates for the Flow of a Viscous Incompressible Fluid down an Inclined Plane in the Thin Film Regime
Hiroki Ueno, Akinori Shiraishi, Tatsuo Iguchi
We consider a two-dimensional motion of a thin film flowing down an inclined plane under the influence of the gravity and the surface tension. In order to investigate the stability…
Motion of a Vortex Filament with Axial Flow in the Half Space
Masashi Aiki, Tatsuo Iguchi
We consider a nonlinear third order dispersive equation which models the motion of a vortex filament immersed in an incompressible and inviscid fluid occupying the three dimensiona…
Solvability of an Initial-Boundary Value Problem for a Second Order Parabolic System with a Third Order Dispersion Term
Masashi Aiki, Tatsuo Iguchi
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…
Motion of a Vortex Filament in the Half Space
Masashi Aiki, Tatsuo Iguchi
A model equation for the motion of a vortex filament immersed in three dimensional, incompressible and inviscid fluid is investigated as a humble attempt to model the motion of a t…