Journal of Mathematical Physics, ISSN 0022-2488, 10/2018, Volume 59, Issue 10, p. 102502

In recent studies, we have constructed axisymmetric solutions to the Euler-Poisson equations which give mathematical models of slowly uniformly rotating...

EXISTENCE | GENERAL-RELATIVITY | PHYSICS, MATHEMATICAL | POST-NEWTONIAN EXPANSIONS | Mathematics - Analysis of PDEs

EXISTENCE | GENERAL-RELATIVITY | PHYSICS, MATHEMATICAL | POST-NEWTONIAN EXPANSIONS | Mathematics - Analysis of PDEs

Journal Article

2.
Full Text
An application of the Nash–Moser theorem to the vacuum boundary problem of gaseous stars

Journal of Differential Equations, ISSN 0022-0396, 01/2017, Volume 262, Issue 2, pp. 803 - 843

We have been studying spherically symmetric motions of gaseous stars with physical vacuum boundary governed either by the Euler–Poisson equations in the...

Nash–Moser theory | Vacuum boundary | Spherically symmetric solutions | Gaseous stars | Non-linear hyperbolic equations | MATHEMATICS | COMPRESSIBLE EULER EQUATIONS | PHYSICAL VACUUM | Nash-Moser theory | SPHERICALLY SYMMETRIC MOTIONS | WELL-POSEDNESS | Mathematics - Analysis of PDEs

Nash–Moser theory | Vacuum boundary | Spherically symmetric solutions | Gaseous stars | Non-linear hyperbolic equations | MATHEMATICS | COMPRESSIBLE EULER EQUATIONS | PHYSICAL VACUUM | Nash-Moser theory | SPHERICALLY SYMMETRIC MOTIONS | WELL-POSEDNESS | Mathematics - Analysis of PDEs

Journal Article

Funkcialaj Ekvacioj. Serio Internacia, ISSN 0532-8721, 01/2015, Volume 58, Issue 1, p. 43

We consider spherically symmetric motions of inviscid compressible gas surrounding a solid ball under the gravity of the core. Equilibria touch the vacuum...

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 09/2016, Volume 57, Issue 9, p. 1

It is known that spherically symmetric static solutions of the Einstein equations with a positive cosmological constant for the energy-momentum tensor of a...

Energy | Solutions | Cosmology | Mathematics | Symmetry

Energy | Solutions | Cosmology | Mathematics | Symmetry

Journal Article

Kyoto Journal of Mathematics, ISSN 2156-2261, 06/2016, Volume 56, Issue 2, pp. 243 - 282

We construct spherically symmetric solutions to the Einstein-Euler equations, which give models of gaseous stars in the framework of the general theory of...

EXISTENCE | MATHEMATICS | MOTIONS | Mathematics - Analysis of PDEs

EXISTENCE | MATHEMATICS | MOTIONS | Mathematics - Analysis of PDEs

Journal Article

6.
Full Text
On spherically symmetric motions of a gaseous star governed by the euler–poisson equations

Osaka Journal of Mathematics, ISSN 0030-6126, 2015, Volume 52, Issue 2, pp. 545 - 580

We consider spherically symmetric motions of a polytropic gas under the self-gravitation governed by the Euler-Poisson equations. The adiabatic exponent (= the...

MATHEMATICS | PHYSICAL VACUUM | WELL-POSEDNESS | 35L52 | 35L05 | 35L57 | 35L70 | 76L10

MATHEMATICS | PHYSICAL VACUUM | WELL-POSEDNESS | 35L52 | 35L05 | 35L57 | 35L70 | 76L10

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 09/2016, Volume 57, Issue 9, p. 92502

It is known that spherically symmetric static solutions of the Einstein equations with a positive cosmological constant for the energy-momentum tensor of a...

PHYSICS, MATHEMATICAL | FIELD-EQUATIONS | RELATIVITY | Cosmological constant | Einstein equations | Quantum gravity

PHYSICS, MATHEMATICAL | FIELD-EQUATIONS | RELATIVITY | Cosmological constant | Einstein equations | Quantum gravity

Journal Article

Funkcialaj Ekvacioj, ISSN 0532-8721, 2015, Volume 58, Issue 1, pp. 43 - 85

We consider spherically symmetric motions of inviscid compressible gas surrounding a solid ball under the gravity of the core. Equilibria touch the vacuum with...

Vacuum boundary | Nash-Moser theorem | Spherically symmetric solutions | Compressible Euler equations | Compressible euler equations | MATHEMATICS | MATHEMATICS, APPLIED | PHYSICAL VACUUM | WELL-POSEDNESS

Vacuum boundary | Nash-Moser theorem | Spherically symmetric solutions | Compressible Euler equations | Compressible euler equations | MATHEMATICS | MATHEMATICS, APPLIED | PHYSICAL VACUUM | WELL-POSEDNESS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 03/2019, Volume 266, Issue 7, pp. 3942 - 3972

We consider stationary axisymmetric solutions of the Euler–Poisson equations, which govern the internal structure of barotropic gaseous stars. We take the...

Nonlinear integral equation | Euler–Poisson equations | Axisymmetric solutions | Free boundary | Stellar rotation | EXISTENCE | MATHEMATICS | Euler-Poisson equations | STARS | Mathematics - Analysis of PDEs

Nonlinear integral equation | Euler–Poisson equations | Axisymmetric solutions | Free boundary | Stellar rotation | EXISTENCE | MATHEMATICS | Euler-Poisson equations | STARS | Mathematics - Analysis of PDEs

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 08/2017, Volume 225, Issue 2, pp. 873 - 900

We construct stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of polytropic gaseous stars, with small...

LANE-EMDEN STARS | EXISTENCE | VACUUM | MATHEMATICS, APPLIED | MECHANICS | Mathematics - Analysis of PDEs

LANE-EMDEN STARS | EXISTENCE | VACUUM | MATHEMATICS, APPLIED | MECHANICS | Mathematics - Analysis of PDEs

Journal Article

08/2019

We consider the equations for the coefficients of stationary rotating axisymmetric metrics governed by the Einstein-Euler equations, that is, the Einstein...

Journal Article

07/2019

Axially symmetric stationary metrics governed by the Einstein-Euler equations for slowly rotating perfect fluids have been constructed in an arbitrarily large...

Journal Article

02/2019

The linearized operator for non-radial oscillations of spherically symmetric self-gravitating gaseous stars is analyzed in view of the functional analysis. The...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

Annali dell’Università di Ferrara, ISSN 0430-3202, 12/2002, Volume 48, Issue 1, pp. 1 - 20

Si considera un problema di frontiera libera per l’equazione del moto unidimensionale isoentropico con viscosità dipendente dalla densità secondo la legge μ =b...

existence | a free boundary problem | Mathematics | History of Mathematics | Geometry | a global weak solution | uniqueness | Analysis | Numerical Analysis | Mathematics, general | Algebraic Geometry | density-dependent viscosity | isentropic gas

existence | a free boundary problem | Mathematics | History of Mathematics | Geometry | a global weak solution | uniqueness | Analysis | Numerical Analysis | Mathematics, general | Algebraic Geometry | density-dependent viscosity | isentropic gas

Journal Article

15.
Full Text
Note on the descriptions of the Euler-Poisson equations in various co-ordinate systems

01/2017

In this note we derive the descriptions of the system of Euler-Poisson equations which governs the hydrodynamic evolution of gaseous stars in various...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

16.
Full Text
On a certain type of nonlinear hyperbolic equations derived from astrophysical problems

01/2016

Investigations of spherically symmetric motions of self-gravitating gaseous stars governed by the non-relativistic Newtonian gravitation theory or by the...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

10/2018

The hydrodynamic evolution of self-gravitating gaseous stars is governed by the Euler-Poisson equations. We study the structure of the linear approximation of...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

09/2015

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...

Journal Article

09/2015

We construct spherically symmetric solutions to the Einstein-Euler equations, which contains a positive cosmological constant, say, the Einstein-Euler-de...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

08/2015

Spherically symmetric static solutions of the Einstein equations with a positive cosmological constant for the energy-momentum tensor of a barotropic perfect...

Journal Article

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