## Differential and Integral Equations

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

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

#### 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