TY - JOUR
T1 - Non-existence and non-uniqueness for multidimensional sticky particle systems
AU - Bressan, Alberto
AU - Nguyen, Truyen
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014/6
Y1 - 2014/6
N2 - 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.
AB - 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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U2 - 10.3934/krm.2014.7.205
DO - 10.3934/krm.2014.7.205
M3 - Article
AN - SCOPUS:84898967459
SN - 1937-5093
VL - 7
SP - 205
EP - 218
JO - Kinetic and Related Models
JF - Kinetic and Related Models
IS - 2
ER -