The p-system II: The vacuum

Robin Young

Banach Center Publications (2003)

  • Volume: 60, Issue: 1, page 237-252
  • ISSN: 0137-6934

Abstract

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We consider the equations of isentropic gas dynamics in Lagrangian coordinates. We are interested in global interactions of large waves, and their relation to global solvability and well-posedness for large data. One of the main difficulties in this program is the possible occurrence of a vacuum, in which the specific volume is infinite. In this paper we show that the vacuum cannot be generated in finite time. More precisely, if the vacuum is present for some positive time, then it must be present in the initial data, in a precise sense which is given. We also discuss the annihilation of vacuums that are present in the initial data.

How to cite

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Robin Young. "The p-system II: The vacuum." Banach Center Publications 60.1 (2003): 237-252. <http://eudml.org/doc/281954>.

@article{RobinYoung2003,
abstract = {We consider the equations of isentropic gas dynamics in Lagrangian coordinates. We are interested in global interactions of large waves, and their relation to global solvability and well-posedness for large data. One of the main difficulties in this program is the possible occurrence of a vacuum, in which the specific volume is infinite. In this paper we show that the vacuum cannot be generated in finite time. More precisely, if the vacuum is present for some positive time, then it must be present in the initial data, in a precise sense which is given. We also discuss the annihilation of vacuums that are present in the initial data.},
author = {Robin Young},
journal = {Banach Center Publications},
keywords = {isentropic gas equation; Riemann problem; rarefaction wave; vacuum; Lagrangian coordinates},
language = {eng},
number = {1},
pages = {237-252},
title = {The p-system II: The vacuum},
url = {http://eudml.org/doc/281954},
volume = {60},
year = {2003},
}

TY - JOUR
AU - Robin Young
TI - The p-system II: The vacuum
JO - Banach Center Publications
PY - 2003
VL - 60
IS - 1
SP - 237
EP - 252
AB - We consider the equations of isentropic gas dynamics in Lagrangian coordinates. We are interested in global interactions of large waves, and their relation to global solvability and well-posedness for large data. One of the main difficulties in this program is the possible occurrence of a vacuum, in which the specific volume is infinite. In this paper we show that the vacuum cannot be generated in finite time. More precisely, if the vacuum is present for some positive time, then it must be present in the initial data, in a precise sense which is given. We also discuss the annihilation of vacuums that are present in the initial data.
LA - eng
KW - isentropic gas equation; Riemann problem; rarefaction wave; vacuum; Lagrangian coordinates
UR - http://eudml.org/doc/281954
ER -

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