Local exponential attractors for models of phase change for compressible gas dynamics

A. Eden, A. Milani, B. Nicolaenko

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The authors investigate a model for dynamic phase transitions in a van der Waals compressible fluid. As the pressure is given by a nonconvex equation of state, which also blows up for a finite volume, the corresponding initial value problem is of mixed hyperbolic-elliptic type. Therefore, it generates nontrivial dynamics. The system of conservation laws when regularized with capillarity terms excludes the appearance of shocks but keeps most of the interesting dynamics. By introducing the appropriate Hamiltonian function, local invariant domains are constructed that avoid the blow-up and at the same time allow solutions of mixed type. They show that, even in regions of mixed type, the initial value problem exhibits finite-dimensional dynamical behaviour by establishing the existence of local attractors and of exponential attractors of finite fractal dimension.

Original languageEnglish
Article number007
Pages (from-to)93-117
Number of pages25
JournalNonlinearity
Volume6
Issue number1
DOIs
Publication statusPublished - Dec 1 1993

Fingerprint

Exponential Attractors
Gas dynamics
gas dynamics
Phase Change
Gas Dynamics
Initial value problems
boundary value problems
Blow-up
Initial Value Problem
Hamiltonian functions
Hamiltonians
Capillarity
compressible fluids
Systems of Conservation Laws
Van Der Waals
Compressible Fluid
Fractal dimension
conservation laws
Equations of state
Finite Volume

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

@article{f44a3b5b8a61454cbe6d1a37dc7ad66f,
title = "Local exponential attractors for models of phase change for compressible gas dynamics",
abstract = "The authors investigate a model for dynamic phase transitions in a van der Waals compressible fluid. As the pressure is given by a nonconvex equation of state, which also blows up for a finite volume, the corresponding initial value problem is of mixed hyperbolic-elliptic type. Therefore, it generates nontrivial dynamics. The system of conservation laws when regularized with capillarity terms excludes the appearance of shocks but keeps most of the interesting dynamics. By introducing the appropriate Hamiltonian function, local invariant domains are constructed that avoid the blow-up and at the same time allow solutions of mixed type. They show that, even in regions of mixed type, the initial value problem exhibits finite-dimensional dynamical behaviour by establishing the existence of local attractors and of exponential attractors of finite fractal dimension.",
author = "A. Eden and A. Milani and B. Nicolaenko",
year = "1993",
month = "12",
day = "1",
doi = "10.1088/0951-7715/6/1/007",
language = "English",
volume = "6",
pages = "93--117",
journal = "Nonlinearity",
issn = "0951-7715",
publisher = "IOP Publishing Ltd.",
number = "1",

}

Local exponential attractors for models of phase change for compressible gas dynamics. / Eden, A.; Milani, A.; Nicolaenko, B.

In: Nonlinearity, Vol. 6, No. 1, 007, 01.12.1993, p. 93-117.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Local exponential attractors for models of phase change for compressible gas dynamics

AU - Eden, A.

AU - Milani, A.

AU - Nicolaenko, B.

PY - 1993/12/1

Y1 - 1993/12/1

N2 - The authors investigate a model for dynamic phase transitions in a van der Waals compressible fluid. As the pressure is given by a nonconvex equation of state, which also blows up for a finite volume, the corresponding initial value problem is of mixed hyperbolic-elliptic type. Therefore, it generates nontrivial dynamics. The system of conservation laws when regularized with capillarity terms excludes the appearance of shocks but keeps most of the interesting dynamics. By introducing the appropriate Hamiltonian function, local invariant domains are constructed that avoid the blow-up and at the same time allow solutions of mixed type. They show that, even in regions of mixed type, the initial value problem exhibits finite-dimensional dynamical behaviour by establishing the existence of local attractors and of exponential attractors of finite fractal dimension.

AB - The authors investigate a model for dynamic phase transitions in a van der Waals compressible fluid. As the pressure is given by a nonconvex equation of state, which also blows up for a finite volume, the corresponding initial value problem is of mixed hyperbolic-elliptic type. Therefore, it generates nontrivial dynamics. The system of conservation laws when regularized with capillarity terms excludes the appearance of shocks but keeps most of the interesting dynamics. By introducing the appropriate Hamiltonian function, local invariant domains are constructed that avoid the blow-up and at the same time allow solutions of mixed type. They show that, even in regions of mixed type, the initial value problem exhibits finite-dimensional dynamical behaviour by establishing the existence of local attractors and of exponential attractors of finite fractal dimension.

UR - http://www.scopus.com/inward/record.url?scp=0043049052&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0043049052&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/6/1/007

DO - 10.1088/0951-7715/6/1/007

M3 - Article

AN - SCOPUS:0043049052

VL - 6

SP - 93

EP - 117

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 1

M1 - 007

ER -