Kinetic and Related Models (KRM)

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

Pages: 205 - 218, Volume 7, Issue 2, June 2014      doi:10.3934/krm.2014.7.205

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Alberto Bressan - Department of Mathematics, Penn State University, University Park, Pa.16802, United States (email)
Truyen Nguyen - Department of Mathematics, University of Akron, Akron, OH 44325, United States (email)

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.

Keywords:  Sticky particle systems, pressureless Euler system, non-existence, non-uniqueness, conservation laws.
Mathematics Subject Classification:  Primary: 35L03, 35L65, 35L80; Secondary: 70F16.

Received: December 2013;      Revised: February 2014;      Available Online: March 2014.