Non-existence and non-uniqueness for multidimensional sticky particle systems

Alberto Bressan; Truyen Nguyen

doi:10.3934/krm.2014.7.205

Article Contents

2014, Volume 7, Issue 2: 205-218. Doi: 10.3934/krm.2014.7.205

This issue Previous Article Next Article Gas-surface interaction and boundary conditions for the Boltzmann equation

Non-existence and non-uniqueness for multidimensional sticky particle systems

Alberto Bressan^1, and
Truyen Nguyen^2,

1.
Department of Mathematics, Penn State University, University Park, Pa.16802
2.
Department of Mathematics, University of Akron, Akron, OH 44325

Received: November 30, 2013

Revised: January 31, 2014

Published: May 2014

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Abstract

The paper is concerned with sticky weak solutions to the equations of pressureless gases in two or more space dimensions. Various initial data are constructed, showing that the Cauchy problem can have (i) two distinct sticky solutions, or (ii) no sticky solution, not even locally in time. In both cases the initial density is smooth with compact support, while the initial velocity field is continuous.

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Mathematics Subject Classification: Primary: 35L03, 35L65, 35L80; Secondary: 70F16.

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