Differential and Integral Equations

An existence theorem in the large for zero-pressure gas dynamics

Michael Sever

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Abstract

We obtain existence of a weak solution of the equations of zero-pressure gas dynamics, in any number of space dimensions plus time, given initial data of finite mass and kinetic energy. Our solution satisfies the "sticky particle" or adhesion dynamics conditions. The argument depends on a definition of a weak solution based on the introduction of Lagrangian coordinates and in particular on an application of the entropy condition proposed by C. Dafermos for hyperbolic systems of conservation laws.

Article information

Source
Differential Integral Equations, Volume 14, Number 9 (2001), 1077-1092.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356124308

Mathematical Reviews number (MathSciNet)
MR1852872

Zentralblatt MATH identifier
1023.35068

Subjects
Primary: 35L65: Conservation laws
Secondary: 35L67: Shocks and singularities [See also 58Kxx, 76L05] 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30] 85A40: Cosmology {For relativistic cosmology, see 83F05}

Citation

Sever, Michael. An existence theorem in the large for zero-pressure gas dynamics. Differential Integral Equations 14 (2001), no. 9, 1077--1092. https://projecteuclid.org/euclid.die/1356124308


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