Nonlinear stability of expanding star solutions of the radially-symmetric mass-critical Euler-Poisson system

Mahir Hadzic; Juhi Jang

doi:10.1002/cpa.21721

Nonlinear stability of expanding star solutions of the radially-symmetric mass-critical Euler-Poisson system

Mahir Hadzic, Juhi Jang

USC University of Southern California

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Abstract

We prove nonlinear stability of compactly supported expanding star-solutions of the mass-critical gravitational Euler-Poisson system. These special solutions were discovered by Goldreich and Weber in 1980. The expanding rate of such solutions can be either self-similar or non-self-similar (linear), and we treat both types. An important outcome of our stability results is the existence of a new class of global-in-time radially symmetric solutions, which are not homogeneous and therefore not encompassed by the existing works. Using Lagrangian coordinates we reformulate the associated free-boundary problem as a degenerate quasilinear wave equation on a compact spatial domain. The problem is mass-critical with respect to an invariant rescaling and the analysis is carried out in similarity variables.

Original language	English
Number of pages	65
Journal	COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
Early online date	27 Oct 2017
DOIs	https://doi.org/10.1002/cpa.21721
Publication status	E-pub ahead of print - 27 Oct 2017

Keywords

Euler-Poisson system
Nonlinear stability
Free boundary problem
Fluid mechanics

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10.1002/cpa.21721

Nonlinear stability of expanding_HADZIC_Accepted28November2016_GREEN AAMAccepted author manuscript, 389 KB

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title = "Nonlinear stability of expanding star solutions of the radially-symmetric mass-critical Euler-Poisson system",

abstract = "We prove nonlinear stability of compactly supported expanding star-solutions of the mass-critical gravitational Euler-Poisson system. These special solutions were discovered by Goldreich and Weber in 1980. The expanding rate of such solutions can be either self-similar or non-self-similar (linear), and we treat both types. An important outcome of our stability results is the existence of a new class of global-in-time radially symmetric solutions, which are not homogeneous and therefore not encompassed by the existing works. Using Lagrangian coordinates we reformulate the associated free-boundary problem as a degenerate quasilinear wave equation on a compact spatial domain. The problem is mass-critical with respect to an invariant rescaling and the analysis is carried out in similarity variables.",

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AU - Hadzic, Mahir

AU - Jang, Juhi

PY - 2017/10/27

Y1 - 2017/10/27

N2 - We prove nonlinear stability of compactly supported expanding star-solutions of the mass-critical gravitational Euler-Poisson system. These special solutions were discovered by Goldreich and Weber in 1980. The expanding rate of such solutions can be either self-similar or non-self-similar (linear), and we treat both types. An important outcome of our stability results is the existence of a new class of global-in-time radially symmetric solutions, which are not homogeneous and therefore not encompassed by the existing works. Using Lagrangian coordinates we reformulate the associated free-boundary problem as a degenerate quasilinear wave equation on a compact spatial domain. The problem is mass-critical with respect to an invariant rescaling and the analysis is carried out in similarity variables.

AB - We prove nonlinear stability of compactly supported expanding star-solutions of the mass-critical gravitational Euler-Poisson system. These special solutions were discovered by Goldreich and Weber in 1980. The expanding rate of such solutions can be either self-similar or non-self-similar (linear), and we treat both types. An important outcome of our stability results is the existence of a new class of global-in-time radially symmetric solutions, which are not homogeneous and therefore not encompassed by the existing works. Using Lagrangian coordinates we reformulate the associated free-boundary problem as a degenerate quasilinear wave equation on a compact spatial domain. The problem is mass-critical with respect to an invariant rescaling and the analysis is carried out in similarity variables.

KW - Euler-Poisson system

KW - Nonlinear stability

KW - Free boundary problem

KW - Fluid mechanics

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DO - 10.1002/cpa.21721

M3 - Article

SN - 0010-3640

JO - COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

JF - COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

ER -

Nonlinear stability of expanding star solutions of the radially-symmetric mass-critical Euler-Poisson system

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Keywords

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