Formation of singularities of solutions of the equations of motion of compressible fluids subjected to external forces in the case of several spatial variables |
| |
Authors: | O S Rozanova |
| |
Institution: | (1) Department of Differential Equations, Mathematics and Mechanics Faculty, Moscow State University, Vorobiovy Gory, 119992 Moscow, Russia |
| |
Abstract: | One considers a class of solutions with finite total energy and moment of inertia for the equations of motion of compressible
fluids. It is shown that for a wide class of right-hand sides, including the viscosity term, initially smooth solutions may
acquire singularities on a finite time interval. A sufficient condition for the appearance of singularities is found. This
condition may be called “the best possible sufficient condition” in the sense that one can explicitly construct a time-global
smooth solution for which this condition does not hold to within arbitrary infinitely small quantities. For a nontrivial constant
state, perturbations with compact support are considered. A generalization is proved for the known theorem on the initial
conditions for which the solution acquires singularities on a finite time interval. The effect of dry friction and rotation
on the formation of singularities of smooth solutions is examined.
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 26, pp. 274–308, 2007. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|