Formation of singularities in solutions to ideal hydrodynamics of freely cooling inelastic gases

被引:3
作者
Rozanova, Olga [1 ,2 ]
机构
[1] Moscow MV Lomonosov State Univ, Dept Differential Equat & Mech, Moscow 119992, Russia
[2] Moscow MV Lomonosov State Univ, Fac Math, Moscow 119992, Russia
关键词
CAUCHY-PROBLEM;
D O I
10.1088/0951-7715/25/6/1547
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider solutions to the hyperbolic system of equations of ideal granular hydrodynamics with conserved mass, total energy and finite momentum of inertia and prove that these solutions generically lose the initial smoothness within a finite time in any space dimension n. Furthermore, in the one-dimensional case we introduce a solution depending only on the spatial coordinate outside of a ball containing the origin and prove that this solution under rather general assumptions on initial data cannot be global in time too. Then we construct an exact axially symmetric solution with separable time and space variables having a strong singularity in the density component beginning from the initial moment of time, whereas other components of solution are initially continuous.
引用
收藏
页码:1547 / 1558
页数:12
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