28 citations · 106 across the 24 of their papers we have counts for
24 papers
On the essential spectrum of adiabatic stellar oscillations
Tetu Makino
The generator of the linearized evolution equation of adiabatic oscillations of a gaseous star, ELASO, is a second order integro-differential operator and is realized…
Linearized Analysis of Adiabatic Oscillations of Rotating Gaseous Stars
Tetu Makino
We study adiabatic oscillations of rotating self-gravitating gaseous stars in mathematically rigorous manner. The internal motion of the star is supposed to be governed by the Eule…
On a mathematical model of the rotating atmosphere of the Earth
Tetu Makino
In meteorology the analysis of motions of the atmosphere on the Earth has been done using various mathematical models and using various approximations. In this article as the simpl…
On the axisymmetric metric generated by a rotating perfect fluid with the vacuum boundary
Tetu Makino
We consider the equations for the coefficients of stationary rotating axisymmetric metrics governed by the Einstein-Euler equations, that is, the Einstein equations together with t…
On Adiabatic Oscillations of a Stratified Atmosphere on the Flat Earth
Tetu Makino
We consider the oscillations of the atmosphere around a stratified back ground density and entropy distribution under the gravitation on the flat Earth. The atmosphere is supposed…
On Incompressible Vibrations of the Stratified Atmosphere on the Flat Earth
Tetu Makino
We consider the vibrations and waves in the atmosphere under the gravitation on the flat earth. The stratified density distribution of the back ground equilibrium is supposed to to…
A Note on the Axisymmetric Stationary Metric in the General Theory of Relativity
Tetu Makino
We consider the equations for the coefficients of stationary rotating axisymmetric metrics governed by the Einstein-Euler equations, that is, the Einstein equations together with t…
A Remark on the Matter-Vacuum Matching Problem for Axisymmetric Metrics Governed by the Einstein-Euler Equations
Tetu Makino
Axially symmetric stationary metrics governed by the Einstein-Euler equations for slowly rotating perfect fluids have been constructed in an arbitrarily large bounded domain contai…
On Linear Adiabatic Perturbations of Spherically Symmetric Gaseous Stars Governed by the Euler-Poisson Equations
Tetu Makino
The linearized operator for non-radial oscillations of spherically symmetric self-gravitating gaseous stars is analyzed in view of the functional analysis. The evolution of the sta…
Linearized Analysis of Barotropic Perturbations around Spherically Symmetric Gaseous Stars Governed by the Euler-Poisson Equations
Juhi Jang, Tetu Makino
The hydrodynamic evolution of self-gravitating gaseous stars is governed by the Euler-Poisson equations. We study the structure of the linear approximation of barotropic perturbati…
On Rotating Axisymmetric Solutions of the Euler-Poisson Equations
Juhi Jang, Tetu Makino
We consider stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of barotropic gaseous stars. We take the general form of the equat…
On slowly rotating axisymmetric solutions of the Einstein-Euler equations
Tetu Makino
In recent works we have constructed axisymmetric solutions to the Euler-Poisson equations which give mathematical models of slowly uniformly rotating gaseous stars. We try to exten…
Note on the descriptions of the Euler-Poisson equations in various co-ordinate systems
Tetu Makino
In this note we derive the descriptions of the system of Euler-Poisson equations which governs the hydrodynamic evolution of gaseous stars in various co-ordinate systems. This note…
On slowly rotating axisymmetric solutions of the Euler-Poisson equations
Juhi Jang, Tetu Makino
We construct stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of polytropic gaseous stars, with small constant angular velocity…
An Application of the Nash-Moser Theorem to the Vacuum Boundary Problem of Gaseous Stars
Tetu Makino
We have been studying spherically symmetric motions of gaseous stars with physical vacuum boundary governed either by the Euler-Poisson equations in the non-relativistic theory or…
On a certain type of nonlinear hyperbolic equations derived from astrophysical problems
Tetu Makino
Investigations of spherically symmetric motions of self-gravitating gaseous stars governed by the non-relativistic Newtonian gravitation theory or by the general relativistic theor…
On the time evolution of a homogeneous isotropic gaseous universe
Tetu Makino
We investigate the time evolution of a homogeneous isotropic universe which consists of a perfect gas governed by the Einstein-Euler-de Sitter equations. Under suitable assumptions…
On spherically symmetric solutions of the Einstein-Euler-de Sitter equations
Tetu Makino
We construct spherically symmetric solutions to the Einstein-Euler equations, which contains a positive cosmological constant, say, the Einstein-Euler-de Sitter equations. We assum…
On the Tolman-Oppenheimer-Volkoff-de Sitter equation
Tetu Makino
Spherically symmetric static solutions of the Einstein equations with a positive cosmological constant for the energy-momentum tensor of a barotropic perfect fluid are governed by…
On Spherically Symmetric Solutions of the Einstein-Euler Equations
Tetu Makino
We construct spherically symmetric solutions to the Einstein-Euler equations, which give models of gaseous stars in the framework of the general theory of relativity. We assume a r…
A Note on a Modified Catuskoti
Tetu Makino
The `catuskoti' or tetralemma in Buddhist logic is a problematic subject from the modern logical point of view. Recently a many-valued paraconsistent logic was proposed in order to…
On spherically symmetric motions of a gaseous star governed by the Euler-Poisson equations
Tetu Makino
We study spherically symmetric motions of a gaseous star governed by the Euler-Poisson equations. Equilibria are given as solutions of the Lane-Emden equations, and the linearized…
On Spherically Symmetric Motions of the Atmosphere Surrounding a Planet Governed by the Compressible Euler Equations
Tetu Makino
We consider spherically symmetric motions of inviscid compressible gas surrounding a solid ball under the gravity of the core. Equilibria touch the vacuum with finite radii, and th…
An Application of Nash-Moser Theorem to Smooth Solutions of One-Dimensional Compressible Euler Equation with Gravity
Cheng-Hsiung Hsu, Song-Sun Lin, Tetu Makino +1
We study one-dimensional motions of polytropic gas governed by the compressible Euler equations. The problem on the half space under a constant gravity gives an equilibrium which h…